Question

write the equation of the line in fully simplified slope-intercept form.
answer
attempt 1 out of 2

Explanation:

Step1: Identify slope-intercept form

Slope-intercept form is \( y = mx + b \), where \( m \) is slope and \( b \) is y-intercept.

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

The line crosses y-axis at \( (0, -5) \), so \( b = -5 \).

Step3: Calculate slope (\( m \))

Use two points, e.g., \( (0, -5) \) and \( (4, 1) \). Slope \( m = \frac{1 - (-5)}{4 - 0} = \frac{6}{4} = \frac{3}{2} \).

Step4: Write equation

Substitute \( m = \frac{3}{2} \) and \( b = -5 \) into \( y = mx + b \): \( y = \frac{3}{2}x - 5 \).

Answer:

\( y = \frac{3}{2}x - 5 \)