Question

graph the line with the equation $y = \frac{2}{5}x - 6$.

Explanation:

Step1: Find the y - intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=\frac{2}{5}x - 6\), when \(x = 0\), \(y=-6\). So, one point is \((0,-6)\).

Step2: Use the slope to find another point

The slope \(m=\frac{2}{5}\). From the point \((0,-6)\), using the slope formula \(\text{slope}=\frac{\Delta y}{\Delta x}\), if \(\Delta x = 5\), then \(\Delta y=2\). So, another point is \((0 + 5,-6+2)=(5,-4)\).

Step3: Plot the points and draw the line

Plot the points \((0,-6)\) and \((5,-4)\) on the coordinate plane. Then draw a straight line passing through these two points.

Answer:

Plot the points \((0,-6)\) and \((5,-4)\) and draw a line through them to graph \(y = \frac{2}{5}x-6\).