Question

graph the line with the equation $y = \frac{2}{5}x - 2$.

Explanation:

Step1: Find the y - intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=\frac{2}{5}x - 2\), when \(x = 0\), \(y=-2\). So, plot the point \((0,-2)\).

Step2: Use the slope to find another point

The slope \(m=\frac{2}{5}\). From the point \((0,-2)\), move up \(2\) units (rise) and then move right \(5\) units (run). So, from \((0,-2)\), we get the point \((0 + 5,-2+2)=(5,0)\).

Step3: Draw the line

Connect the two points \((0,-2)\) and \((5,0)\) with a straight line and extend it in both directions.

Answer:

Plot the point \((0,-2)\) (y - intercept), then use the slope \(\frac{2}{5}\) (rise \(2\), run \(5\)) from \((0,-2)\) to get \((5,0)\), and draw a line through these two points.