Question

which graph represents the equation $12 = 3x + 4y$?
a
b
c
explain how you know.
$3x$ is on x-intercept line and the $4y$ is on the y-intercept line.

Explanation:

Step1: Rewrite to slope-intercept form

Rearrange $12=3x+4y$ to $y=mx+b$:

$$\begin{align*} 4y&=-3x+12\\ y&=-\frac{3}{4}x+3 \end{align*}$$

Step2: Find x-intercept (y=0)

Set $y=0$, solve for $x$:

$$\begin{align*} 0&=-\frac{3}{4}x+3\\ \frac{3}{4}x&=3\\ x&=4 \end{align*}$$

Step3: Find y-intercept (x=0)

Set $x=0$, solve for $y$:

$$ y=-\frac{3}{4}(0)+3=3 $$

Step4: Match to graph

The line has a negative slope, x-intercept $(4,0)$, y-intercept $(0,3)$, which matches Graph A.

The equation $12=3x+4y$ is rewritten to slope-intercept form $y=-\frac{3}{4}x+3$, showing a negative slope. Calculating intercepts gives $(4,0)$ (x-intercept) and $(0,3)$ (y-intercept), which corresponds to Graph A.

Answer:

A (the graph with a downward-sloping line crossing the x-axis at (4,0) and y-axis at (0,3))