Question

y + 3 = \frac{4}{3}(x + 3)

Explanation:

Step1: Solve the equation \( y + 3=\frac{4}{3}(x + 3) \) for \( y \)

First, distribute the \(\frac{4}{3}\) on the right side: \( y+3=\frac{4}{3}x + 4 \)
Then, subtract 3 from both sides: \( y=\frac{4}{3}x + 4 - 3 \), so \( y=\frac{4}{3}x+1 \)

Step2: Find two points on the line

• When \( x = 0 \), \( y=\frac{4}{3}(0)+1 = 1 \), so the point is \( (0,1) \)
• When \( x = 3 \), \( y=\frac{4}{3}(3)+1=4 + 1=5 \), so the point is \( (3,5) \)

Step3: Plot the points and draw the line

Plot the points \( (0,1) \) and \( (3,5) \) on the coordinate plane and draw a straight line through them.

Answer:

The line \( y=\frac{4}{3}x + 1 \) can be graphed by plotting the points \( (0,1) \) and \( (3,5) \) (or other points found from the equation) and drawing a line through them.