Slope Intercept to Standard Form
How to convert from y = mx + b to Ax + By = C
more interesting facts
It is a common to ask to have to convert equation of line from slope intercept to standard form , as demonstrated by the pictures below.
Example of Converting from Slope Intercept to Standard Form
Convert $$ y = \frac 5 4 x + 5 $$, graphed on the right, to standard form.
Multiply by the least common denominator of the fractions (if any)
The only fraction is $$ \frac { 5}{ \red 4} $$ so you can multiply everything by 4. $ \red 4 \cdot y = \red 4 \cdot \big( \frac { 5}{ \red 4}x +5 \big) \\ 4y = 5x + 20 $
Move" y 1 to the other side by adding its opposite to both sides of the equation and simplify
Solve for the y-intercept (or " b " in the slope intercept equation) which is 20 in this example.
Use our Calculator
You can use the calculator below to find the equation of a line from any two points. Just type numbers into the boxes below and the calculator (which has its own page here ) will automatically calculate the equation of line in standard and slope intercept forms
( Try this 'equation from 2 points' calculator on its own page here . )
Practice Problems
Convert the the equation below from slope intercept form to standard form $$ y = \frac 2 3 x -4 $$
Multiply by the least common denominator of the fractions
The only fraction is $$ \frac{2}{\red 3 } $$ so you can multiply everything by 3.
$$ \red 3 \cdot y = \red 3 \big( \frac{2}{\red 3 } -4 \big) \\ 3y = 2x-12 $$
Solve for the y-intercept (or " b " in the slope intercept equation) which is 12 in this problem.
Change the the equation below from slope intercept to standard from $$ y = \frac 1 2 x + 5 $$
The only fraction is $$ \frac{1}{\red 2}$$ so you can multiply everything by 2.
$$ \red 2 \cdot y =\red 2 \cdot \big( \frac{1}{\red 2} x + 5 \big) \\2y = x + 10 $$
Solve for the y-intercept (or " b " in the slope intercept equation) which is 10 in this problem.
Convert the the equation below from slope intercept to standard from $$ y = \frac 2 3 x + \frac 5 9 $$
Multiply all terms by the least common denominator of the fractions
Unlike the prior examples, this problem has two fractions $$ \big( \frac 2 3 \text{ and } \frac 5 9 \big) $$ so you can multiply everything by their common denominator of $$ \red 9$$ .
$$ \red 9 \cdot y = \red 9 \big( \frac 2 3 x + \frac 5 9 \big) \\ 9y = 6x + 5 $$
Solve for the y-intercept (or " b " in the slope intercept equation) which, in this example, is 5.
Convert the the equation below from slope intercept to standard from $$ y = 5x + \frac 4 7 $$
This problem only has the fraction $$ \frac{4}{\red 7 } $$ so we must multiply everything by 7.
$$ \red 7 \cdot y = \red 7 \big( 5x + \frac 4 7 \big) \\ 7y = 35x + 4 $$
Solve for the y-intercept (or " b " in the slope intercept equation) which, in this example, is 4.
Convert the the equation below from slope intercept to standard from (yes, this is a very challenging problem so let's see how sharp your algebra skills are.) $ y = ax + \frac b c $
This problem only has the fraction $$ \frac{b}{ \red c } $$ so we must multiply everything by $$ \red c $$.
$$ \red c \cdot y = \red c \big( ax + \frac b c \big) \\ cy = cax + b $$ .
Solve for the y-intercept (or " b " in the slope intercept equation) which, in this example, is the variable 'b'.
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| x^{\msquare} | \log_{\msquare} | \sqrt{\square} | \nthroot[\msquare]{\square} | \le | \ge | \frac{\msquare}{\msquare} | \cdot | \div | x^{\circ} | \pi | |||||||||||
| \left(\square\right)^{'} | \frac{d}{dx} | \frac{\partial}{\partial x} | \int | \int_{\msquare}^{\msquare} | \lim | \sum | \infty | \theta | (f\:\circ\:g) | f(x) | |||||||||||
| - \twostack{▭}{▭} | \lt | 7 | 8 | 9 | \div | AC |
| + \twostack{▭}{▭} | \gt | 4 | 5 | 6 | \times | \square\frac{\square}{\square} |
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Course: Algebra 1 > Unit 5
- Intro to linear equation standard form
- Graphing a linear equation: 5x+2y=20
- Clarifying standard form rules
- Graph from linear standard form
- Converting from slope-intercept to standard form
- Convert linear equations to standard form
Standard form review
What is the linear standard form?
Finding features and graph from standard equation.
- Your answer should be
- an integer, like 6
- a simplified proper fraction, like 3 / 5
- a simplified improper fraction, like 7 / 4
- a mixed number, like 1 3 / 4
- an exact decimal, like 0.75
- a multiple of pi, like 12 pi or 2 / 3 pi
Converting to standard form
- (Choice A) 2 x + y = − 2 A 2 x + y = − 2
- (Choice B) 7 y = − 14 x − 2 B 7 y = − 14 x − 2
- (Choice C) 14 x + 7 y = − 2 C 14 x + 7 y = − 2
- (Choice D) 7 x + 7 y = 2 D 7 x + 7 y = 2
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IMAGES
COMMENTS
A relationship that has a straight line graph. point-slope form. the equation of a straight line in the form y − y1 = m (x − x1) rise. The vertical change between any two points on a line. run. The horizontal change between any two points on a line. slope-intercept form. An equation written in the form y=mx+ b, where m is the slope and b is ...
It's quite easy. Slope-intercept form: y = mx + b. The "m" is the slope. The "b" is the y-intercept. So, if the problem tells you the slope = 3/4 and the y-intercept is -5, then you can create the equation by: -- swap out "m" and put in 3/4. -- swap out "b" and put in -5. You get the equation: y = 3/4 (x) - 5.
So the way that it's written right now, this is slope intercept form. It's written in the form Y is equal to mx plus b, where m in this case is 2/3 and b is 4/7. It's very easy to figure out what the slope and what the Y intercept is from this equation. But we wanna write this in standard form.
Slope m = (y2-y1)/ (x2-x1) If you mulitply both sides by (x2-x1), then you get point slope form: (y2-y1) = m (x2-x1) Then, they swab a couple of variables to clarify the variables that stay. X2 becomes X, and Y2 becomes Y. And, you have the point slope form. Remember, slope is calculated as the change in Y over the change in X.
Free worksheet(pdf) and answer key on slope intercept form. 29 scaffolded questions that start relatively easy and end with some real challenges. Plus model problems explained step by step. Math Gifs; ... Slope Intercept to Standard Form; Standard to Slope Intercept; Interactive Slope: explore the formula of slope by clicking and dragging two ...
Terms in this set (12) y = 4x + 5. Write the equation of the line that passes through (1, 9) with a slope of 4. y = -2x + 10. Write the equation of the line that passes through (4, 2) with a slope of -2. y = 5x - 15. Write the equation of the line that passes through (3, 0) with a slope of 5. y = x - 3.
2 3 4 In your own words, what is slope-intercept form? Slope-intercept form is the equation of a straight line in the form of y = mx+b where m is the slope and b is the y-intercept. Write the following equation in slope-intercept form: 3y + 6x = 18 -6x -6x 3y = -6x + 18 3 3 3 y = -2x + 6 Write the following equation
Further, the slope is − 7 / 3, so m = − 7 / 3. Substitute these numbers into the slope-intercept form of the line. y = mx + b Slope-intercept form. y = − 7 3x + 2 Substitute: − 7 / 3 for m, 2 for b. Therefore, the slope-intercept form of the line is y = − 7 3x + 2. Label the line with this equation.
This keystroke exercise lets students discover the connection between the parent and family of functions so they can quickly graph functions of the form y=mx+b. 5. Possible answers for comparing the graph of Y=X to Y=X+1: parallel, equivalent slope, offset by 1, Y=X crosses the origin (0,0), etc. 7.
Example of Converting from Slope Intercept to Standard Form. Example. Convert $$ y = \frac 5 4 x + 5 $$, graphed on the right, to standard form. Show Answer. Step 1. Multiply by the least common denominator of the fractions (if any) step 1 answer.
1. slope: Mathematics 9 Linear Relations Slope-Intercept Form Part 2 ratio of the vertical change (rise) to the horizontal change (run) of a line or a line segment. Rise Slope = Run the y-coordinate of the point where a line or curve crosses the y-axis. It is the value of y when x 2. y-intercept: Determininq Slope and Y-intercept Examples
This Linear Functions and Systems Unit Bundle includes guided notes, homework assignments, two quizzes, a study guide and a unit test that cover the following topics: • Domain and Range of a Relation. • Relations vs. Functions. • Evaluating Functions. • Linear Equations: Standard Form vs. Slope-Intercept Form. • Graphing by Slope ...
Recall that the slope of a line is the ratio of the change in y over the change in x between any two points on the line: Slope = Change in y Change in x. Therefore, this is the slope between the points ( 0, 3) and ( 2, 7) : m = Change in y Change in x = 7 − 3 2 − 0 = 4 2 = 2. In conclusion, the equation of the line is y = 2 x + 3 .
Free slope intercept form calculator - find the slope intercept form of a line given two points, a function or the intercept step-by-step We've updated our ... Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution. Physics. Mechanics ...
Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Mathway. Visit Mathway on the web ... Find the Slope and y-Intercept. ... The slope-intercept form is , where is the slope and is the y-intercept. Step 2. Find the values of ...
Homework help; Understand a topic; Writing & citations; Tools. Expert Q&A; ... 4-2 Practice Writing Equations in Standard and Slope-Intercept Form Write an equation in point-slope form for the line that passes through each point with the given slope. ... ,m=-3 (-3,-4),m=0 (1,-6),m=-1 (1,3),m=-(3)/(4) Write each equation in standard form. y-11=3 ...
Unit 2: Linear Functions Date: Bell: Homework 3: Writing Linear Equations, Applications, & Linear Regression **This is a 2-page documenti ** Point Slope & Two Points: Write a linear equation in slope-intercept form with the given Information 1. slope = -6; passes through (-4,1) 2. slope = passes through (-5, -6) 3. passes through (-4, 11) and (2,8) 4. passes through (6, 3) and (14,-5) Linear ...
The slope-intercept form of a linear equation is where one side contains just "y". So, it will look like: y = mx + b where "m" and "b" are numbers. This form of the equation is very useful. The coefficient of "x" (the "m" value) is the slope of the line. And, the constant (the "b" value) is the y-intercept at (0, b)
Final answer: In mathematics, slope-intercept form and standard form are two ways to represent linear equations. Slope-intercept form is written as y = mx + b, where m represents the slope of the line and b represents the y-intercept. Standard form is written as Ax + By = C, where A, B, and C are constants and A and B are not both zero.
Slope-intercept form is a linear equation in which y is isolated and is written as y = mx + b. Here, m is the slope of the line and b is the y-intercept of the line. The slope of the line is the ratio of the rise (vertical change) to the run (horizontal change) between any two points on the line. So, the slope of a line can be written as: Slope ...
Browse slope intercept form and standard form foldable resources on Teachers Pay Teachers, a marketplace trusted by millions of teachers for original educational resources.
When we have a linear equation in standard form, we can find the x - and y -intercepts of the corresponding line. This also allows us to graph it. Consider, for example, the equation 2 x + 3 y = 12 . If we set x = 0 , we get the equation 3 y = 12 , and we can quickly tell that y = 4 , which means the y -intercept is ( 0, 4) . In a similar way ...
Standard form shows the x and the y on one side with their respective coefficients. So, for example, x + y = 5. Every x and y pair that you plug in which makes this true forms a point on a graph, and if you draw a line through these points it is a perfect straight line.