Question

8.
(2, 7)
(-1, -8)
m =
b =
equation:

Explanation:

Step1: Calculate the slope \( m \)

The formula for slope \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Let \( (x_1, y_1) = (-1, -8) \) and \( (x_2, y_2) = (2, 7) \). Then \( m = \frac{7 - (-8)}{2 - (-1)} = \frac{15}{3} = 5 \).

Step2: Find the y-intercept \( b \)

Use the slope-intercept form \( y = mx + b \). Substitute \( m = 5 \) and one of the points, say \( (2, 7) \), into the equation: \( 7 = 5(2) + b \). Solve for \( b \): \( 7 = 10 + b \), so \( b = 7 - 10 = -3 \).

Step3: Write the equation

Using \( m = 5 \) and \( b = -3 \), the equation is \( y = 5x - 3 \).

Answer:

\( m = 5 \)
\( b = -3 \)
Equation: \( y = 5x - 3 \)