Question

Find the slope of the line that passes through each pair of points
A(4, 5) and B(–3, 5)

S(3, –6) and T(3, –9)

Answer 1

Answer:

A and B: slope = 0

S and T: slope = undefined    

Step-by-step explanation:

To find the slope of the line that passes between a pair of points, use the slope formula, $m = \frac{y_2-y_1}{x_2-x_1}$. Substitute the x and y values of two points into that formula and simplify.

1) Let's try this with the first problem. Substitute the x and y values of (4,5) and (-3,5) into the formula, then solve:

$m = \frac{(5)-(5)}{(-3)-(4)}\\m = \frac{5-5}{-3-4} \\m = \frac{0}{-7} \\m = 0$

So, the slope of the line between A and B is 0.

2) Do the same with the second problem, substituting the x and y values of (3,-6) and (3,-9):

$m = \frac{(-9)-(-6)}{(3)-(3)} \\m = \frac{-9+6}{3-3} \\m = \frac{-3}{0}$

However, we can't divide by zero. So, the slope between points S and T must be undefined.