Question

write the equation of the line in fully simplified slope-intercept form.

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 \( (0, 4) \), so \( b = 4 \).

Step3: Calculate slope (\( m \))

Use points \( (0, 4) \) and \( (4, 0) \). Slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{0 - 4}{4 - 0}=\frac{-4}{4}=-1 \).

Step4: Write the equation

Substitute \( m = -1 \) and \( b = 4 \) into \( y = mx + b \): \( y=-x + 4 \).

Answer:

\( y = -x + 4 \)