Question

graph this line using the slope and y-intercept:
$y = \frac{1}{2}x - 10$
click to select points on the graph.

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 \(y=\frac{1}{2}x - 10\), the slope \(m=\frac{1}{2}\) and the y - intercept \(b=- 10\).

Step2: Plot the y - intercept

The y - intercept is the point where \(x = 0\). So, when \(x = 0\), \(y=-10\). Plot the point \((0,-10)\) on the graph.

Step3: Use the slope to find another point

The slope \(m=\frac{1}{2}=\frac{\text{rise}}{\text{run}}\). This means from the point \((0, - 10)\), we move up 1 unit (rise) and then move to the right 2 units (run). So, starting from \((0,-10)\), moving up 1 and right 2 gives us the point \((0 + 2,-10+1)=(2,-9)\). We can also move down 1 and left 2 (since \(\frac{- 1}{-2}=\frac{1}{2}\)) from \((0,-10)\) to get \((-2,-11)\), but moving up and right is more intuitive for graphing.

Step4: Draw the line

After plotting the y - intercept \((0,-10)\) and another point (for example, \((2,-9)\) or other points found using the slope), draw a straight line passing through these points.

Answer:

To graph the line \(y = \frac{1}{2}x-10\):

1. Plot the y - intercept at \((0,-10)\) (since when \(x = 0\), \(y=-10\)).
2. Use the slope \(\frac{1}{2}\) (rise = 1, run = 2). From \((0,-10)\), move up 1 unit and right 2 units to get the point \((2,-9)\) (or other points using the slope).
3. Draw a straight line through the plotted points \((0,-10)\) and \((2,-9)\) (and other points generated by the slope) to represent the line.