Question

write the equation of this line in slope-intercept form.

Explanation:

Step1: Identify the y-intercept

The line crosses the y-axis at (0, 4), so the y-intercept \( b = 4 \).

Step2: Calculate the slope

Use two points, e.g., (0, 4) and (-6, 0). The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Substituting values: \( m=\frac{4 - 0}{0 - (-6)}=\frac{4}{6}=\frac{2}{3} \).

Step3: Write the equation

Slope - intercept form is \( y = mx + b \). Substituting \( m=\frac{2}{3} \) and \( b = 4 \), we get \( y=\frac{2}{3}x + 4 \).

Answer:

\( y=\frac{2}{3}x + 4 \)