Question

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

Explanation:

Step1: Identify slope and intercept

From the graph, the y - intercept \( b = 7 \) (where the line crosses the y - axis). To find the slope \( m \), use two points. Let's take \((0,7)\) and \((2, - 3)\). The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1}\). So \( m=\frac{-3 - 7}{2 - 0}=\frac{-10}{2}=- 5 \).

Step2: Write slope - intercept form

The slope - intercept form of a line is \( y=mx + b \). Substitute \( m=-5 \) and \( b = 7 \) into the formula.

Answer:

\( y=-5x + 7 \)