Question

graph the line with the equation $y = -\frac{1}{2}x - 6$.

Explanation:

Step1: Identify 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 \(y=-\frac{1}{2}x - 6\), the slope \(m =-\frac{1}{2}\) and the y - intercept \(b=- 6\). So, the line crosses the y - axis at \((0,-6)\).

Step2: Plot the y - intercept

Locate the point \((0,-6)\) on the coordinate plane.

Step3: Use the slope to find another point

The slope \(m =-\frac{1}{2}=\frac{\text{rise}}{\text{run}}\). From the point \((0,-6)\), we can go down 1 unit (since rise is - 1) and then to the right 2 units (since run is 2) to get the point \((2,-7)\), or we can go up 1 unit and to the left 2 units to get the point \((- 2,-5)\).

Step4: Draw the line

Connect the points \((0,-6)\) and the other point (e.g., \((2,-7)\) or \((-2,-5)\)) with a straight line.

Answer:

To graph the line \(y =-\frac{1}{2}x-6\):

1. Plot the y - intercept at \((0, - 6)\).
2. Use the slope \(-\frac{1}{2}\) to find another point (e.g., from \((0,-6)\), move down 1 and right 2 to \((2,-7)\) or up 1 and left 2 to \((-2,-5)\)).
3. Draw a straight line through the plotted points.