Question

graph this line using the slope and y-intercept:
$y = \frac{1}{8}x + 4$
click to select points on the graph.
(there is a coordinate grid with x-axis from -10 to 10 and y-axis from -10 to 10)

Explanation:

Step1: Identify y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=\frac{1}{8}x + 4\), \(b = 4\). So the y - intercept is at the point \((0,4)\).

Step2: Use slope to find another point

The slope \(m=\frac{1}{8}\), which means for a run of 8 (change in \(x\)), the rise is 1 (change in \(y\)). Starting from \((0,4)\), if we move 8 units to the right (increase \(x\) by 8) and 1 unit up (increase \(y\) by 1), we get the point \((0 + 8,4+1)=(8,5)\). We can also move in the opposite direction: from \((0,4)\), move 8 units to the left (decrease \(x\) by 8) and 1 unit down (decrease \(y\) by 1) to get \((0 - 8,4 - 1)=(-8,3)\).

Step3: Graph the line

Plot the points \((0,4)\), \((8,5)\) (or \((-8,3)\)) and draw a straight line through them.

Answer:

To graph the line \(y=\frac{1}{8}x + 4\):

1. Plot the y - intercept at \((0,4)\) (since when \(x = 0\), \(y=4\)).
2. Use the slope \(\frac{1}{8}\) (rise = 1, run = 8) to find another point. From \((0,4)\), moving 8 units right and 1 unit up gives \((8,5)\), or 8 units left and 1 unit down gives \((-8,3)\).
3. Draw a straight line through the plotted points.