Question

1. identify the slope and y-intercept in each equation below then graph.

a. $y = -\frac{3}{5}x + 2$
b. $y = 4x - 5$

1. solve each equation below for y. show your work.

a. $2x - 3y = 12$

Explanation:

(10a):

Step1: Match to slope-intercept form

Slope-intercept form: $y=mx+b$, where $m$=slope, $b$=y-intercept.
For $y=-\frac{3}{5}x+2$, $m=-\frac{3}{5}$, $b=2$.

Step2: Verify graph points

• Y-intercept: $(0,2)$
• Use slope: from $(0,2)$, move 5 right, 3 down to $(5,-1)$; move 3 left, 5 up to $(-5,5)$. These match the given graph.

(10b):

Step1: Match to slope-intercept form

For $y=4x-5$, $m=4$, $b=-5$.

Step2: Identify graph points

• Y-intercept: $(0,-5)$
• Use slope: from $(0,-5)$, move 1 right, 4 up to $(1,-1)$; move 1 left, 4 down to $(-1,-9)$.

(11a):

Step1: Isolate $-3y$ term

Subtract $2x$ from both sides:
$2x-3y-2x=12-2x$
$-3y=12-2x$

Step2: Solve for $y$

Divide all terms by $-3$:
$y=\frac{12-2x}{-3}$
$y=\frac{2}{3}x-4$

Answer:

10a. Slope: $\boldsymbol{-\frac{3}{5}}$, Y-intercept: $\boldsymbol{(0,2)}$ (graph matches the line through $(0,2)$, $(5,-1)$, $(-5,5)$)
10b. Slope: $\boldsymbol{4}$, Y-intercept: $\boldsymbol{(0,-5)}$ (graph the line through $(0,-5)$ and $(1,-1)$)
11a. $\boldsymbol{y=\frac{2}{3}x-4}$