Question

1. write the equation in slope-intercept form for the line that passes through (-2,1) and has a slope of -3. then, verify if the point (1, -8) is a solution to the equation.

Explanation:

Step1: Use point-slope form

Point-slope form: \( y - y_1 = m(x - x_1) \), where \( (x_1,y_1)=(-2,1) \), \( m=-3 \).
Substitute: \( y - 1 = -3(x - (-2)) \) → \( y - 1 = -3(x + 2) \)

Step2: Convert to slope-intercept form

Expand: \( y - 1 = -3x - 6 \). Add 1: \( y = -3x - 5 \)

Step3: Verify (1, -8)

Substitute \( x=1 \): \( y = -3(1) -5 = -8 \), which matches the y-value. So it is a solution.

Answer:

The equation is \( y = -3x - 5 \); (1, -8) is a solution.