Question

y = -\frac{1}{3}x + 2, try again

Explanation:

Step1: Identify the y - intercept

The equation of the line is in slope - intercept form \(y = mx + b\), where \(b\) is the y - intercept. For the equation \(y=-\frac{1}{3}x + 2\), the y - intercept \(b = 2\). So, the line passes through the point \((0,2)\), which is already plotted on the graph.

Step2: Use the slope to find another point

The slope \(m=-\frac{1}{3}\). The slope is defined as \(\frac{\text{change in }y}{\text{change in }x}\), so for a slope of \(-\frac{1}{3}\), we can move 1 unit down (negative change in \(y\)) and 3 units to the right (positive change in \(x\)) from the point \((0,2)\).
Starting from \((0,2)\), if we move 1 unit down, \(y = 2- 1=1\), and 3 units to the right, \(x=0 + 3 = 3\). So, the point \((3,1)\) is on the line.
Or we can move 3 units to the left (negative change in \(x\)) and 1 unit up (positive change in \(y\)) from \((0,2)\). Moving 3 units left, \(x = 0-3=-3\), and 1 unit up, \(y=2 + 1 = 3\). So, the point \((- 3,3)\) is also on the line.

Step3: Draw the line

Using the two points (e.g., \((0,2)\) and \((3,1)\) or \((0,2)\) and \((-3,3)\)), we can draw a straight line passing through them.

To plot the line \(y =-\frac{1}{3}x + 2\):

1. Start with the y - intercept \((0,2)\) (already plotted).
2. Use the slope \(m =-\frac{1}{3}\): from \((0,2)\), move 3 units right and 1 unit down to get \((3,1)\), or 3 units left and 1 unit up to get \((-3,3)\).
3. Draw a straight line through these points.

Answer:

To graph \(y =-\frac{1}{3}x+2\), plot the y - intercept \((0,2)\) (already done) and then use the slope \(-\frac{1}{3}\) to find another point (e.g., \((3,1)\) or \((-3,3)\)) and draw a line through these points.