Question

graph the line.
$y = -\frac{1}{5}x + 6$

Explanation:

Step1: Identify the y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For \(y=-\frac{1}{5}x + 6\), \(b = 6\). So the line crosses the y - axis at \((0,6)\). Mark the point \((0,6)\) on the graph.

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 down 1 unit (decrease in \(y\) by 1). From the point \((0,6)\), if we move \(x = 5\) (to \(x=5\)), then \(y=6 - 1=5\), so we get the point \((5,5)\). We can also move left 5 units ( \(x=- 5\)) and up 1 unit ( \(y = 6+1 = 7\)) to get the point \((-5,7)\).

Step3: Draw the line

Connect the points (e.g., \((0,6)\) and \((5,5)\) or other points found using the slope) with a straight line and extend it in both directions.

Answer:

To graph \(y =-\frac{1}{5}x + 6\), first plot the y - intercept \((0,6)\). Then use the slope \(m =-\frac{1}{5}\) to find another point (e.g., from \((0,6)\), move 5 units right and 1 unit down to get \((5,5)\)) and draw a straight line through these points, extending it in both directions.