Question

question
what is the slope of the line that goes through the points (-2,5) and (0,2)?
select the correct answer.
m = 1/2
m = -1/2
m = -3/2
m = 3/2

Explanation:

Step1: Recall slope formula

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

Step2: Identify coordinates

Let \( (x_1, y_1)=(-2, 5) \) and \( (x_2, y_2)=(0, 2) \).

Step3: Substitute into formula

Substitute values: \( m=\frac{2 - 5}{0 - (-2)}=\frac{-3}{2}=-\frac{3}{2} \)? Wait, no, wait, the options have \( -\frac{3}{2} \)? Wait, no, the points are (-2,5) and (0,2). So \( y_2 - y_1 = 2 - 5=-3 \), \( x_2 - x_1 = 0 - (-2)=2 \). So \( m=\frac{-3}{2}=-\frac{3}{2} \)? Wait, but the options: let me check again. Wait, maybe I misread the points. Wait, the points are (-2,5) and (0,2). So \( x_1=-2, y_1=5 \); \( x_2=0, y_2=2 \). Then slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{2 - 5}{0 - (-2)}=\frac{-3}{2}=-\frac{3}{2} \). Wait, but the options: the second option is \( m = -\frac{3}{2} \)? Wait, the user's options: first option \( m=\frac{3}{2} \), second \( m = -\frac{3}{2} \), third \( m = -\frac{1}{2} \), fourth \( m=\frac{1}{2} \)? Wait, no, maybe I made a mistake. Wait, no, let's recalculate. Wait, (0,2) and (-2,5). So the change in y is 2 - 5 = -3, change in x is 0 - (-2) = 2. So slope is -3/2. So the correct option is the second one, \( m = -\frac{3}{2} \).

Answer:

The correct answer is the option with \( m = -\frac{3}{2} \) (assuming the second option is \( m = -\frac{3}{2} \), e.g., if the options are:
A. \( m=\frac{3}{2} \)
B. \( m = -\frac{3}{2} \)
C. \( m = -\frac{1}{2} \)
D. \( m=\frac{1}{2} \)

Then the answer is B. \( m = -\frac{3}{2} \)