Question

1. what is the slope of a line that passes through points (-2, 1) and (-4, 9)

Explanation:

Step1: Recall the slope formula

The slope \( m \) of a line passing through 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 coordinates

Let \( (x_1, y_1)=(-2, 1) \) and \( (x_2, y_2)=(-4, 9) \).

Step3: Substitute into the formula

Substitute the values into the slope formula: \( m=\frac{9 - 1}{-4 - (-2)} \).

Step4: Simplify the numerator and denominator

Simplify the numerator: \( 9 - 1 = 8 \).
Simplify the denominator: \( -4 - (-2)=-4 + 2=-2 \).

Step5: Calculate the slope

Now, \( m=\frac{8}{-2}=-4 \).

Answer:

The slope of the line is \(-4\).