Question

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

Explanation:

Step1: Identify the slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For \(y=-\frac{1}{6}x + 1\), the y - intercept \(b = 1\), so the line crosses the y - axis at \((0,1)\). The slope \(m=-\frac{1}{6}\), which means for every 6 units we move to the right along the x - axis, we move down 1 unit, or for every 6 units we move to the left, we move up 1 unit.

Step2: Plot the y - intercept

Locate the point \((0,1)\) on the coordinate plane.

Step3: Use the slope to find another point

From \((0,1)\), using the slope \(m =-\frac{1}{6}\), we can move 6 units to the right (increase \(x\) by 6) and 1 unit down (decrease \(y\) by 1). So \(x=0 + 6=6\) and \(y = 1-1 = 0\), giving the point \((6,0)\). Or we can move 6 units to the left (decrease \(x\) by 6) and 1 unit up (increase \(y\) by 1). So \(x=0-6=-6\) and \(y = 1 + 1=2\), giving the point \((-6,2)\).

Step4: Draw the line

Connect the points (for example, \((0,1)\) and \((6,0)\) or \((0,1)\) and \((-6,2)\)) with a straight line.

Answer:

To graph \(y =-\frac{1}{6}x + 1\), plot the y - intercept \((0,1)\), then use the slope \(-\frac{1}{6}\) to find another point (e.g., \((6,0)\) or \((-6,2)\)) and draw a straight line through these points.