Question

Find the slope of the line passing through the points (-7,8) and (-7,-6)

Answer 1

Answer:

1) undefined

2) 0

Step-by-step explanation:

Slope formula:

$m=\frac{y2-y1}{x2-x1}$

Problem 1:

(x1, y1) = (-7, 8)

(x2, y2) = (-7, -6)

Plug those 2 points into the slope formula and solve:

$m=\frac{-6-8}{-7--7}\\\\m=\frac{-14}{0}$

Here, you can't divide by 0, so this slope is undefined. An undefined slope would make a completely vertical line on a graph. In this case, the equation of the line would be just:

$x=-7$

Problem 2:

(x1, y1) = (-9, -8)

(x2, y2) = (3, -8)

$m=\frac{-8--8}{3--9}\\\\m=\frac{0}{12}\\\\m=0$

The slope is 0, and that would make a horizontal line on a graph. The equation would be:

$y=-8$

You don't actually need to fully work out the slope that way. If you ever have 2 points with the same x-coordinate, the slope has to be undefined. If you ever have 2 points with the same y-coordinate, then the slope has to be 0, assuming it's linear of course. You can see that in the points given, the first 2 have the same x and the second 2 have the same y.