Question

select the correct answer. what is the slope of the line that goes through (-5,-5) and (5,-7)? a. $-\frac{1}{5}$ b. 0 c. $\frac{1}{5}$ d. undefined

Explanation:

Step1: Recall the slope formula

The slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify the points

Let \( (x_1, y_1)=(-5, -5) \) and \( (x_2, y_2)=(5, -7) \).

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m=\frac{-7 - (-5)}{5 - (-5)} \).

Step4: Simplify the numerator and denominator

Simplify the numerator: \( -7 - (-5)=-7 + 5=-2 \).
Simplify the denominator: \( 5 - (-5)=5 + 5 = 10 \).
So, \( m=\frac{-2}{10}=-\frac{1}{5} \). Wait, there is a mistake here. Wait, let's recalculate. Wait, the second point: is it (5, -7)? Wait, the user's problem: through (-5,-5) and (5,-7)? Wait, no, maybe I misread. Wait, the options have -1/5? Wait, no, let's check again. Wait, maybe the second point is (5, -5)? No, the problem says (5,-7). Wait, no, let's do it again. \( y_2 - y_1=-7 - (-5)=-7 + 5=-2 \). \( x_2 - x_1=5 - (-5)=10 \). So \( m=\frac{-2}{10}=-\frac{1}{5} \). But wait, the option A is -1/5? Wait, the options: A. -1/5, B. 0, C. 1/5, D. undefined. So the correct calculation: slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{-7 - (-5)}{5 - (-5)}=\frac{-2}{10}=-\frac{1}{5} \). So the answer is A? Wait, but let's check again. Wait, maybe the second point is (5, -5)? No, the problem says (5,-7). Wait, maybe I made a mistake. Wait, no, let's confirm. If the points are (-5, -5) and (5, -5), then slope is 0, but here it's (5, -7). Wait, no, the user's problem: "through (-5,-5) and (5,-7)". So the calculation is correct. So the slope is -2/10 = -1/5. So the answer is A.

Answer:

A. \(-\frac{1}{5}\)