Question

1. 3x - 2y = 12
2. 4x + 5y = 20

Explanation:

Step1: Rewrite 3x-2y=12 to slope-intercept form

Solve for $y$:

$$\begin{align*} 3x - 2y &= 12 \\ -2y &= -3x + 12 \\ y &= \frac{3}{2}x - 6 \end{align*}$$

Step2: Find intercepts for 3x-2y=12

• x-intercept (set $y=0$):

$3x = 12 \implies x=4$, so point $(4, 0)$

• y-intercept (set $x=0$):

$-2y=12 \implies y=-6$, so point $(0, -6)$

Step3: Rewrite 4x+5y=20 to slope-intercept form

Solve for $y$:

$$\begin{align*} 4x + 5y &= 20 \\ 5y &= -4x + 20 \\ y &= -\frac{4}{5}x + 4 \end{align*}$$

Step4: Find intercepts for 4x+5y=20

• x-intercept (set $y=0$):

$4x=20 \implies x=5$, so point $(5, 0)$

• y-intercept (set $x=0$):

$5y=20 \implies y=4$, so point $(0, 4)$

Answer:

1. For $3x-2y=12$:

• Plot points $(4, 0)$ and $(0, -6)$, then draw a straight line through them. The line has a slope of $\frac{3}{2}$.

1. For $4x+5y=20$:

• Plot points $(5, 0)$ and $(0, 4)$, then draw a straight line through them. The line has a slope of $-\frac{4}{5}$.