Question

1. plot all points that fall on the line

$y = \frac{2}{3}x + 4$

Explanation:

Step1: Identify y-intercept

The y-intercept occurs at $x=0$. Substitute $x=0$ into the equation:
$y = \frac{2}{3}(0) + 4 = 4$
This gives the point $(0, 4)$.

Step2: Find a second point

Choose $x=3$ to eliminate the fraction. Substitute $x=3$:
$y = \frac{2}{3}(3) + 4 = 2 + 4 = 6$
This gives the point $(3, 6)$.

Step3: Find a third point

Choose $x=-3$ for a negative x-value. Substitute $x=-3$:
$y = \frac{2}{3}(-3) + 4 = -2 + 4 = 2$
This gives the point $(-3, 2)$.

Step4: Define the line

The line passes through all points satisfying $y=\frac{2}{3}x+4$; plotting the above points and drawing a straight line through them will represent all such points.

Answer:

Key points on the line include $(0, 4)$, $(3, 6)$, and $(-3, 2)$. Draw a straight line through these points to plot all points on $y=\frac{2}{3}x+4$.