Question

graph the line.
$y = -\frac{2}{5}x - 3$

Explanation:

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For \(y=-\frac{2}{5}x - 3\), the slope \(m =-\frac{2}{5}\) and the y - intercept \(b=- 3\).

Step2: Plot the y-intercept

The y - intercept is \(-3\), so we plot the point \((0,-3)\) on the y - axis.

Step3: Use the slope to find another point

The slope \(m =-\frac{2}{5}=\frac{\text{rise}}{\text{run}}\). From the point \((0, - 3)\), we move down 2 units (because the rise is - 2) and then 5 units to the right (because the run is 5). This gives us the point \((5,-5)\). We can also move up 2 units and 5 units to the left from \((0,-3)\) to get the point \((- 5,-1)\).

Step4: Draw the line

Connect the points \((0,-3)\), \((5,-5)\) (or \((-5,-1)\)) with a straight line.

Answer:

To graph \(y =-\frac{2}{5}x-3\), plot \((0, - 3)\) (y - intercept), then use the slope \(-\frac{2}{5}\) to find another point (e.g., \((5,-5)\) or \((-5,-1)\)) and draw a line through these points.