# Write an equation of the line that has the given slope and y-intercept

Find the slope and the y-intercept of the line. This example is written in function notation, but is still linear. What is the equation of this line in slope-intercept form? So any line can be represented in slope-intercept form, is y is equal to mx plus b, where this m right over here, that is of the slope of the line.

And this b over here, this is the y-intercept of the line. Let me draw a quick line here just so that we can visualize that a little bit. So that is my y-axis. And then that is my x-axis. And let me draw a line. And since our line here has a negative slope, I'll draw a downward sloping line.

So let's say our line looks something like that. So hopefully, we're a little familiar with the slope already.

The slope essentially tells us, look, start at some point on the line, and go to some other point of the line, measure how much you had to move in the x direction, that is your run, and then measure how much you had to move in the y direction, that is your rise.

And our slope is equal to rise over run. And you can see over here, we'd be downward sloping. Because if you move in the positive x direction, we have to go down.

If our run is positive, our rise here is negative. So this would be a negative over a positive, it would give you a negative number. That makes sense, because we're downward sloping.

The more we go down in this situation, for every step we move to the right, the more downward sloping will be, the more of a negative slope we'll have.

So that's slope right over here. The y-intercept just tells us where we intercept the y-axis. So the y-intercept, this point right over here, this is where the line intersects with the y-axis. This will be the point 0 comma b.

And this actually just falls straight out of this equation. When x is equal to so let's evaluate this equation, when x is equal to 0.

Well, anything times 0 is 0. So y is equal to 0 plus b, or y will be equal to b, when x is equal to 0. So this is the point 0 comma b. Now, they tell us what the slope of this line is. They tell us we go through the-- Let me just, in a new color.

I've already used orange, let me use this green color. They tell us what we go through the point 0 comma 8. Notice, x is 0. So we're on the y-axis. When x is 0, we're on the y-axis. So this is our y-intercept. So b, we could say-- we could do a couple-- our y-intercept is the point 0 comma 8, or we could say that b-- Remember, it's also 0 comma b.

We could say b is equal to 8. And we are done.Converting Equations to the Slope-Intercept Formula. Let’s say we are given an equation in a form other than \(\boldsymbol{y=mx+b}\) and we were asked to graph rutadeltambor.com’s graph the line: \(x=7y+3\) We know that this equation is not in the slope-intercept form, and we must use what we’ve learned about algebra to somehow get it in the form we know.

Example 5: Find an equation of the line that passes through the point (-2, 3) and is parallel to the line 4x + 4y = 8 Solution to Example 5: Let m 1 be the slope of the line whose equation is to be found and m 2 the slope of the given line.

## Lesson Review for Exam 4 - BYU-I Statistics Text

Rewrite the given equation in slope intercept form and find its slope. 4y = -4x + 8 Divide both sides by 4.

After completing this tutorial, you should be able to: Find the slope of a line that is parallel to a given line. Find the slope of a line that is perpendicular to a given line. The equation of a line is typically written as y=mx+b where m is the slope and b is the y-intercept..

If you know the slope (m) any y-intercept (b) of a line, this page will show you how to find the equation of the line. The following questions are intended to help you judge your preparation for the final exam. Carefully work through the problems. These questions are repeated on the preparation quiz for this lesson. by Visitor (United States) Question Find the x-intercept and the y-intercept of the line given by the equation 9x -6y +15 = 0.

Solutions and Explanations to Intermediate Algebra Questions in Sample 1