Question

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

Explanation:

Step1: Identify the y-intercept

The y-intercept (\(b\)) is the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at \((0, 8)\), so \(b = 8\).

Step2: Calculate the slope (\(m\))

We can use two points on the line, e.g., \((0, 8)\) and \((1, 3)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
Substituting the points: \(m=\frac{3 - 8}{1 - 0}=\frac{-5}{1}=-5\).

Step3: Write the equation in slope-intercept form

The slope-intercept form is \(y = mx + b\). Substituting \(m = -5\) and \(b = 8\), we get \(y=-5x + 8\).

Answer:

\(y = -5x + 8\)