Question

which is the slope of the line that passes through the points (-2,4) and (5,-1)?
slope = \frac{3}{7}
slope = -3
slope = -\frac{7}{5}
slope = -\frac{5}{7}

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 points

Given points \((-2, 4)\) (so \( x_1 = -2, y_1 = 4 \)) and \((5, -1)\) (so \( x_2 = 5, y_2 = -1 \)).

Step3: Substitute into formula

Calculate \( y_2 - y_1 = -1 - 4 = -5 \) and \( x_2 - x_1 = 5 - (-2) = 5 + 2 = 7 \). Then \( m = \frac{-5}{7} = -\frac{5}{7} \)? Wait, no, wait: Wait, \( y_2 - y_1 = -1 - 4 = -5 \), \( x_2 - x_1 = 5 - (-2) = 7 \), so \( m = \frac{-5}{7} \)? Wait, no, the options have \( -\frac{5}{7} \)? Wait, the options: let's check again. Wait, the points are \((-2,4)\) and \((5,-1)\). So \( y_2 - y_1 = -1 - 4 = -5 \), \( x_2 - x_1 = 5 - (-2) = 7 \), so slope is \( \frac{-5}{7} = -\frac{5}{7} \)? Wait, but the options: one of them is slope \( = -\frac{5}{7} \)? Wait, the options shown: slope \( = \frac{3}{7} \), slope \( = -3 \), slope \( = -\frac{5}{7} \), slope \( = -\frac{9}{7} \)? Wait, no, the user's image: let's re-express. Wait, the points are \((-2,4)\) and \((5,-1)\). So \( \frac{y2 - y1}{x2 - x1} = \frac{-1 - 4}{5 - (-2)} = \frac{-5}{7} = -\frac{5}{7} \). So the slope is \( -\frac{5}{7} \).

Answer:

The slope is \( -\frac{5}{7} \) (corresponding to the option with slope \( = -\frac{5}{7} \)).