Review slope-intercept form and how to use it to solve problems.

What is slope-intercept form?

Slope-intercept is a specific form of linear equations in two variables:
y=mx+by=\maroonC mx+\greenD b
When an equation is written in this form, m\maroonC m gives the slope of the line and b\greenD b gives its yy-intercept.
Want to learn more about slope-intercept form? Check out this video.

Finding slope-intercept equation from features or graph

Example 1: Equation from slope and intercept

Suppose we want to find the equation of the line whose slope is 1\maroonC{-1} and yy-intercept is (0,5)(0,\greenD5). Well, we simply plug m=1\maroonC{m=-1} and b=5\greenD{b=5} into slope-intercept form!
y=1x+5y=\maroonC{-1}x\greenD{+5}

Example 2: Equation from two points

Suppose we want to find the line that passes through the points (0,4)(0,-4) and (3,1)(3,-1). First, we notice that (0,4)(0,\greenD{-4}) is the yy-intercept. Second, we use the two points to find the slope:
Now we can write the equation in slope-intercept:
y=1x4y=\maroonC{1}x\greenD{-4}
Problem 1
Write the equation of the line whose slope is 55 and yy-intercept is (0,7)(0,-7).
y=y=
Want to try more problems like this? Check out these exercises:

Finding features and graph from slope-intercept equation

When we have a linear equation in slope-intercept form, we can quickly find the slope and yy-intercept of the corresponding line. This also allows us to graph it.
Consider, for example, the equation y=2x+3y=\maroonC2x\greenD{+3}. We can quickly tell that the corresponding line has a slope of 2\maroonC2 and its yy-intercept is (0,3)(0,\greenD{3}). Now we can graph the line:
Problem 1
What is the slope of the line y=3x1y=3x-1?
What is the yy-intercept of the line?
(0,(0,
))
Want to try more problems like this? Check out these exercises:
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