Question

1. graph: $y = \frac{2}{3}x$

Explanation:

Step1: Identify the type of equation

The equation \( y = \frac{2}{3}x \) is a linear equation in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y - intercept. Here, \( b = 0 \) and \( m=\frac{2}{3}\).

Step2: Find two points on the line

• When \( x = 0 \), substitute into the equation: \( y=\frac{2}{3}(0)=0 \). So one point is \( (0,0) \) (the origin).
• When \( x = 3 \), substitute into the equation: \( y=\frac{2}{3}(3)=2 \). So another point is \( (3,2) \).

Step3: Plot the points and draw the line

Plot the points \( (0,0) \) and \( (3,2) \) on the coordinate grid. Then, draw a straight line passing through these two points. The line should have a positive slope (since \( m=\frac{2}{3}>0 \)), meaning it rises from left to right, with a run of 3 (change in \( x \)) and a rise of 2 (change in \( y \)) between consecutive points.

Answer:

To graph \( y=\frac{2}{3}x \), plot the points \((0,0)\) and \((3,2)\) (and other points like \((- 3,-2)\) if needed) and draw a straight line through them. The line passes through the origin, has a slope of \(\frac{2}{3}\) (rises 2 units for every 3 units it runs to the right), and extends infinitely in both directions.