Question

find the equation of the graphed line.
a. $y = -2x + 5$
b. $y = -\frac{2}{5}x + 2$
c. $y = 2x + 5$
d. $y = -\frac{5}{2}x + 5$

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 \((0, 5)\), so \(b = 5\).

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

We can use two points on the line, e.g., \((0, 5)\) and \((2, 1)\) (or \((2.5, 0)\) as the x-intercept). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Using \((0, 5)\) and \((2, 1)\): \(m=\frac{1 - 5}{2 - 0}=\frac{-4}{2}=-2\).

Step3: Write the equation

The slope - intercept form of a line is \(y = mx + b\). Substituting \(m=-2\) and \(b = 5\), we get \(y=-2x + 5\).

Answer:

a. \(y=-2x + 5\)