Question

graph the line with the equation $y = \frac{1}{3}x - 2$.

Explanation:

Step1: Identify slope and y-intercept

The equation is in slope - intercept form \(y = mx + b\), where \(m=\frac{1}{3}\) (slope) and \(b = - 2\) (y - intercept). So the line crosses the y - axis at \((0,-2)\).

Step2: Plot the y - intercept

On the coordinate plane, find the point \((0,-2)\) (2 units below the origin on the y - axis) and mark it.

Step3: Use the slope to find another point

The slope \(m=\frac{1}{3}\) means "rise over run", so from the point \((0,-2)\), we move up 1 unit (rise) and then 3 units to the right (run). This gives us the point \((0 + 3,-2+1)=(3,-1)\). We can also move down 1 unit and 3 units to the left from \((0,-2)\) to get \((0 - 3,-2 - 1)=(-3,-3)\).

Step4: Draw the line

Connect the points (e.g., \((0,-2)\) and \((3,-1)\) or other points found using the slope) with a straight line. The line should extend in both directions.

Answer:

To graph \(y=\frac{1}{3}x - 2\):

1. Plot the y - intercept \((0,-2)\).
2. Use the slope \(\frac{1}{3}\) to find another point (e.g., from \((0,-2)\), move 1 up and 3 right to get \((3,-1)\)).
3. Draw a straight line through the plotted points.