Question

graph this line using the slope and y-intercept:
$y = -\frac{1}{2}x - 9$
click to select points on the graph.

Explanation:

Step1: Identify y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=-\frac{1}{2}x - 9\), \(b=-9\). So the y - intercept is \((0,-9)\).

Step2: Use slope to find another point

The slope \(m =-\frac{1}{2}=\frac{\text{rise}}{\text{run}}\). The rise is \(- 1\) (down 1 unit) and the run is \(2\) (right 2 units) from the y - intercept \((0,-9)\). So starting from \((0,-9)\), moving down 1 and right 2 gives the point \((0 + 2,-9-1)=(2,-10)\). We can also use the rise of \(1\) (up 1 unit) and run of \(-2\) (left 2 units) from \((0,-9)\) to get \((0-2,-9 + 1)=(-2,-8)\).
To graph the line, plot the y - intercept \((0,-9)\) and then use the slope to plot another point (e.g., \((2,-10)\) or \((-2,-8)\)) and draw a straight line through them.

Answer:

To graph \(y =-\frac{1}{2}x-9\):

1. Plot the y - intercept at \((0, - 9)\) (since when \(x = 0\), \(y=-9\)).
2. Use the slope \(m=-\frac{1}{2}\): from \((0,-9)\), move down 1 unit and right 2 units to get the point \((2,-10)\), or move up 1 unit and left 2 units to get the point \((-2,-8)\).
3. Draw a straight line through the plotted points.