Question

1. $y = \frac{-3}{5}x + 4$

Explanation:

Step1: Identify y-intercept

The equation is in slope-intercept form $y=mx+b$, where $b=4$. So the y-intercept is the point $(0, 4)$.

Step2: Use slope to find second point

The slope $m=\frac{-3}{5}$, meaning $\frac{\text{change in } y}{\text{change in } x}=\frac{-3}{5}$. Starting from $(0,4)$, move 5 units right and 3 units down to get the point $(0+5, 4-3)=(5, 1)$.

Step3: Use slope for third point

From $(5,1)$, move another 5 units right and 3 units down: $(5+5, 1-3)=(10, -2)$. We can also go left from $(0,4)$: move 5 units left and 3 units up to get $(0-5, 4+3)=(-5, 7)$.

Step4: Plot and connect points

Plot the points $(0,4)$, $(5,1)$, $(10,-2)$, $(-5,7)$ and draw a straight line through them.

Answer:

The line $y=\frac{-3}{5}x+4$ is graphed by plotting the y-intercept $(0,4)$ and using the slope $\frac{-3}{5}$ to find additional points, then connecting them with a straight line. The key plotted points are $(-5,7)$, $(0,4)$, $(5,1)$, $(10,-2)$.