Question

graph this line using the slope and y - intercept:

$y = \frac{1}{4}x - 8$

click to select points on the graph.

Explanation:

Step1: Identify the \(y\)-intercept

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

Step2: Use the slope to find another point

The slope \(m=\frac{1}{4}\). Using the formula \(\text{slope}=\frac{\Delta y}{\Delta x}\), if \(\Delta x = 4\) (move 4 units to the right from \(x = 0\)), then \(\Delta y=1\). So, \(y=-8 + 1=-7\) and the point is \((4,-7)\).

Step3: Use the slope in the negative direction

If \(\Delta x=-4\) (move 4 units to the left from \(x = 0\)), then \(\Delta y=-1\). So, \(y=-8-1=-9\) and the point is \((-4,-9)\).

Step4: Graph the line

Plot the points \((0,-8)\), \((4,-7)\), and \((-4,-9)\) on the coordinate plane and draw a straight line passing through these points.

Answer:

To graph the line \(y = \frac{1}{4}x - 8\), first plot the \(y\)-intercept at \((0,-8)\). Then, using the slope \(\frac{1}{4}\) (which means for every 4 units we move to the right along the \(x\)-axis, we move 1 unit up along the \(y\)-axis), from the point \((0,-8)\) we can find another point \((4,-7)\) (since \(x = 0+4 = 4\) and \(y=-8 + 1=-7\)). We can also use the slope in the negative direction (for every 4 units we move to the left along the \(x\)-axis, we move 1 unit down along the \(y\)-axis) to find the point \((-4,-9)\) (since \(x=0-4=-4\) and \(y=-8-1 = -9\)). Connect these points to graph the line.