Question

write the equation of this line in slope-intercept form.
write your answer using integers, proper fractions, and improper fractions in simplest form.

Explanation:

Step1: Identify the y-intercept

The line crosses the y-axis at (0, -2), so the y-intercept \( b = -2 \).

Step2: Calculate the slope

Use two points, e.g., (0, -2) and (3, 0). The slope \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - (-2)}{3 - 0} = \frac{2}{3} \).

Step3: Write the equation in slope-intercept form

The slope-intercept form is \( y = mx + b \). Substituting \( m = \frac{2}{3} \) and \( b = -2 \), we get \( y = \frac{2}{3}x - 2 \).

Answer:

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