Question

graph the line.
$y = \frac{1}{3}x$

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = \frac{1}{3}x \) is in slope - intercept form \( y=mx + b \), where \( m=\frac{1}{3} \) (slope) and \( b = 0 \) (y - intercept). So the line passes through the origin \((0,0)\).

Step2: Find another point

To find another point, we can choose a value for \( x \) and calculate \( y \). Let's take \( x = 3 \). Substitute \( x = 3 \) into the equation \( y=\frac{1}{3}x \), we get \( y=\frac{1}{3}\times3=1 \). So the point \((3,1)\) is on the line.

Step3: Graph the line

Plot the points \((0,0)\) and \((3,1)\) on the coordinate plane. Then draw a straight line passing through these two points. The line has a positive slope, so it goes up from left to right.

(Note: Since this is a graphing problem, the final answer is the graph of the line \( y=\frac{1}{3}x \) passing through \((0,0)\) and \((3,1)\) (and other points like \((- 3,-1)\) etc. can also be used for plotting) with a slope of \( \frac{1}{3} \).)

Answer:

The line \( y = \frac{1}{3}x \) is graphed by plotting the points \((0,0)\) and \((3,1)\) (and additional points if needed) and drawing a straight line through them, with a slope of \( \frac{1}{3} \) (rising 1 unit for every 3 units run in the positive x - direction).