Question

a line is graphed in the xy - plane as shown. which of the following is an equation of the line? choose 1 answer: a (y=\frac{2}{5}x + 2) b (y=\frac{2}{5}x - 2) c (y=-\frac{2}{5}x + 2) d (y=-\frac{2}{5}x - 2)

Explanation:

Step1: Determine the slope

The line is decreasing, so the slope \(m\) is negative. The slope - intercept form of a line is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\), the slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points on the line, say \((- 5,0)\) and \((0,-2)\). Then \(m=\frac{-2 - 0}{0-(-5)}=-\frac{2}{5}\).

Step2: Determine the y - intercept

The y - intercept \(b\) is the value of \(y\) when \(x = 0\). From the graph, when \(x = 0\), \(y=-2\).

Step3: Write the equation of the line

Substitute \(m =-\frac{2}{5}\) and \(b=-2\) into \(y=mx + b\), we get \(y =-\frac{2}{5}x-2\).

Answer:

D. \(y =-\frac{2}{5}x - 2\)