Question

graph the line with the equation $y = -\frac{1}{5}x + 2$.

Explanation:

Step1: Identify the slope and y - intercept

The equation of the line is in the slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=-\frac{1}{5}x + 2\), the slope \(m =-\frac{1}{5}\) and the y - intercept \(b = 2\).

Step2: Plot the y - intercept

The y - intercept is \(b = 2\), so we plot the point \((0,2)\) on the y - axis.

Step3: Use the slope to find another point

The slope \(m=-\frac{1}{5}=\frac{\text{rise}}{\text{run}}\). The rise is \(- 1\) (down 1 unit) and the run is \(5\) (right 5 units) from the point \((0,2)\). So, starting from \((0,2)\), moving down 1 unit and right 5 units gives us the point \((0 + 5,2-1)=(5,1)\). We can also use the rise of \(1\) (up 1 unit) and run of \(- 5\) (left 5 units) from \((0,2)\) to get the point \((0-5,2 + 1)=(-5,3)\).

Step4: Draw the line

Draw a straight line through the points \((0,2)\), \((5,1)\) (or \((-5,3)\)) to graph the line \(y =-\frac{1}{5}x+2\).

Answer:

The line is graphed by plotting the y - intercept \((0,2)\) and using the slope \(-\frac{1}{5}\) to find another point (e.g., \((5,1)\) or \((-5,3)\)) and then drawing a straight line through these points. The graph should pass through \((0,2)\) and have a slope of \(-\frac{1}{5}\).