Question

Graph the line that passes through the point (-3,0) and has a slope -3.

Answer 1

See picture below.

Explanation:

First we will find the equation of this said line.

We can use the formula y - y1 = m(x -x1), where (x1, y1) is a point that belongs to the line and m is the slope

In this case we have the point (-3, 0), therefore x1 = -3, y1 = 0, m = -3.

`y-y_(1)=m(x-x_(1) )\\y-0=-3(x-(-3))\\y=-3(x+3)\\y=-3x-9\\`

Therefore, the equation of the line is y = -3x - 9.

We already know that the intersection with the y-axis is (-3,0). To find the intersection with the x-axis we will make x = 0 in the equation.

`y=-3(0)-9\\y=-9`

Therefore, the intersection with the x-axis would be (0,-9)

Now we can take these two points ((0,9), (-3,0)) and draw the line that passes through both of them and we will have the line we're looking for.