Question

graph the line.
$y=\frac{1}{5}x - 4$

Explanation:

Step1: Identify the y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For the equation \(y=\frac{1}{5}x - 4\), the y - intercept \(b=-4\). So, we plot the point \((0,-4)\) on the coordinate plane.

Step2: Determine the slope

The slope \(m=\frac{1}{5}\), which means for every 5 units we move to the right (increase in \(x\) by 5), we move up 1 unit (increase in \(y\) by 1). From the point \((0, - 4)\), if we move 5 units to the right (to \(x = 5\)) and 1 unit up, we reach the point \((5,-4 + 1)=(5,-3)\). We can also move in the opposite direction: from \((0,-4)\), move 5 units to the left (to \(x=-5\)) and 1 unit down, reaching the point \((-5,-4-1)=(-5,-5)\).

Step3: Draw the line

Using the two (or more) points we found (e.g., \((0,-4)\) and \((5,-3)\) or \((0,-4)\) and \((-5,-5)\)), we draw a straight line passing through these points.

Answer:

To graph \(y = \frac{1}{5}x-4\), plot the y - intercept \((0, - 4)\), then use the slope \(\frac{1}{5}\) to find additional points (e.g., \((5,-3)\) or \((-5,-5)\)) and draw a straight line through them. The line should pass through \((0,-4)\) and have a positive, shallow slope.