Question

graph this line using the slope and y-intercept:
$y = \frac{1}{4}x - 10$
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 \(y=\frac{1}{4}x - 10\), \(b=- 10\). So the y - intercept is the point \((0,-10)\).

Step2: Use slope to find another point

The slope \(m=\frac{1}{4}\), which means for a run of \(4\) (change in \(x\)), the rise is \(1\) (change in \(y\)). Starting from \((0,-10)\), if we move \(4\) units to the right (increase \(x\) by \(4\)) and \(1\) unit up (increase \(y\) by \(1\)), we get the point \((0 + 4,-10+1)=(4,-9)\). We can also move in the opposite direction: from \((0,-10)\), move \(4\) units to the left (decrease \(x\) by \(4\)) and \(1\) unit down (decrease \(y\) by \(1\)) to get \((0 - 4,-10 - 1)=(-4,-11)\).

Step3: Graph the line

Plot the points \((0,-10)\), \((4,-9)\) (or other points found using the slope) and draw a straight line through them.

Answer:

To graph the line \(y = \frac{1}{4}x-10\):

1. Plot the y - intercept \((0,-10)\) (since when \(x = 0\), \(y=-10\)).
2. Use the slope \(\frac{1}{4}\) (rise = 1, run = 4) to find another point. For example, from \((0,-10)\), move 4 units right and 1 unit up to get \((4,-9)\), or 4 units left and 1 unit down to get \((-4,-11)\).
3. Draw a straight line through the plotted points.