criosachuga

2023-03-11

How to graph the lines using slope-intercept form $y=-5x$?

Kobe Gentry

Beginner2023-03-12Added 2 answers

The slope-intercept form of a line is $y=mx+b$, where

$m$ = slope , and

$b$ = y-intercept

You must mark two points and connect a line between them in order to graph a line. In the case of using the slope-intercept form, you will be using a point (the y-intercept) and the slope (m) to find the next point.

In this question, we have $y={-}{5}x$. You can see that this is already in the form $y={m}x+b$ and that our slope is $m=-5$.

Now we can look at the y-intercept. We already know that x=0 at the line's intersection with the y-axis because we are examining that location. b, the y-intercept is just 0 since the original equation does not have a value for b. This means that the line crosses the y-axis at the point where y=0, so at the point with coordinates (0,0).

This is where we start (at the point (0,0)). From there, we draw the next point using the slope. We know the slope is -5, and since slope=change in y/change in x, we can say that it is -5/1. This just means that we go 5 units up the y-axis and 1 unit left on the x-axis (since we have a negative sign) from the point y=0. This gives us a new point. Alternatively, we can go 5 units down the y-axis (since we have a negative sign) and 1 unit right. Now that we have two points, we connect them and we have our line. It looks like this:

graph{y=-5x [-10, 10, -5, 5]}

If you have a positive slope, you would either go up the y-axis and right on the x-axis, or down on the y-axis and left on the x-axis.

$m$ = slope , and

$b$ = y-intercept

You must mark two points and connect a line between them in order to graph a line. In the case of using the slope-intercept form, you will be using a point (the y-intercept) and the slope (m) to find the next point.

In this question, we have $y={-}{5}x$. You can see that this is already in the form $y={m}x+b$ and that our slope is $m=-5$.

Now we can look at the y-intercept. We already know that x=0 at the line's intersection with the y-axis because we are examining that location. b, the y-intercept is just 0 since the original equation does not have a value for b. This means that the line crosses the y-axis at the point where y=0, so at the point with coordinates (0,0).

This is where we start (at the point (0,0)). From there, we draw the next point using the slope. We know the slope is -5, and since slope=change in y/change in x, we can say that it is -5/1. This just means that we go 5 units up the y-axis and 1 unit left on the x-axis (since we have a negative sign) from the point y=0. This gives us a new point. Alternatively, we can go 5 units down the y-axis (since we have a negative sign) and 1 unit right. Now that we have two points, we connect them and we have our line. It looks like this:

graph{y=-5x [-10, 10, -5, 5]}

If you have a positive slope, you would either go up the y-axis and right on the x-axis, or down on the y-axis and left on the x-axis.