Questions: Graph the line. y=4/3 x

Transcript text: Graph the line. \[ y=\frac{4}{3} x \]

Solution

Solution Steps

Step 1: Identify the slope and y-intercept

The given equation is \( y = \frac{4}{3}x \). This is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Here, the slope \( m \) is \( \frac{4}{3} \) and the y-intercept \( b \) is 0.

Step 2: Plot the y-intercept

Since the y-intercept \( b \) is 0, the line passes through the origin (0, 0). Plot the point (0, 0) on the graph.

Step 3: Use the slope to find another point

The slope \( \frac{4}{3} \) means that for every 3 units you move to the right on the x-axis, you move 4 units up on the y-axis. Starting from the origin (0, 0), move 3 units to the right to (3, 0) and then 4 units up to (3, 4). Plot the point (3, 4).

Step 4: Draw the line

Draw a straight line through the points (0, 0) and (3, 4).