Question

which is the slope of the line that passes through the points (-2, 4) and (5, -1)?
slope = \frac{2}{3}
slope = -\frac{7}{5}
slope = -3
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 given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \).

Step2: Identify coordinates

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

Step3: Substitute into formula

Substitute the values into the slope formula: \( m=\frac{-1 - 4}{5 - (-2)} \).

Step4: Simplify numerator and denominator

Simplify the numerator: \( -1 - 4=-5 \). Simplify the denominator: \( 5 - (-2)=5 + 2 = 7 \). So \( m=\frac{-5}{7}=-\frac{5}{7} \).

Answer:

slope \( =-\frac{5}{7} \) (the option with this value)