Question

graph the line.
$y = \frac{2}{3}x$

Explanation:

Step1: Identify the slope and y-intercept

The equation \( y = \frac{2}{3}x \) is in slope - intercept form \( y=mx + b \), where \( m=\frac{2}{3} \) (slope) and \( b = 0 \) (y - intercept). So the line passes through the origin \((0,0)\).

Step2: Find another point using the slope

The slope \( m=\frac{2}{3}=\frac{\text{rise}}{\text{run}} \). From the point \((0,0)\), we can move up 2 units (rise) and then 3 units to the right (run). So we get the point \((0 + 3,0+2)=(3,2)\). We can also move down 2 units and 3 units to the left from \((0,0)\) to get \((- 3,-2)\).

Step3: Plot the points and draw the line

Plot the points \((0,0)\), \((3,2)\) (and/or \((-3,-2)\)) on the coordinate plane. Then draw a straight line passing through these points.

(Note: Since the question is about graphing, the final answer is the graph of the line \( y=\frac{2}{3}x \) passing through \((0,0)\), \((3,2)\), \((-3,-2)\) etc. But in terms of the process, the above steps describe how to graph it.)

Answer:

The line \( y = \frac{2}{3}x \) is graphed by plotting the points \((0,0)\) (from the y - intercept \( b = 0\)) and \((3,2)\) (using the slope \( \frac{2}{3}\) to find a second point from the origin) and then drawing a straight line through these points. Other points like \((-3,-2)\) can also be used for accuracy.