Question

1. graph: $y = \frac{4}{3}x$

Explanation:

Step1: Identify the equation type

The equation \( y=\frac{4}{3}x \) is a linear equation in the form \( y = mx \), where \( m=\frac{4}{3} \) (slope) and it passes through the origin \((0,0)\) since there is no \( y \)-intercept (\( b = 0 \)).

Step2: Find two points

• When \( x = 0 \), \( y=\frac{4}{3}(0)=0 \), so the point is \((0,0)\).
• When \( x = 3 \), \( y=\frac{4}{3}(3)=4 \), so the point is \((3,4)\).

Step3: Plot the points

Plot the points \((0,0)\) and \((3,4)\) on the coordinate grid. Then draw a straight line through these two points to represent the graph of \( y=\frac{4}{3}x \).

Answer:

The graph of \( y = \frac{4}{3}x \) is a straight line passing through the origin \((0,0)\) and the point \((3,4)\) (and other points satisfying the equation), drawn by plotting these points and connecting them.