Question

Which equation has the same graph as $4x+8y=12$?

$\begin{array}{c}\text{A.}x+y=3\\ \text{B.}2x+y=3\\ \text{C.}x+2y=3\\ \text{D.}2x+2y=6\end{array}$

Short answer

The equation that has same graph as $4x+8y=12$is option C. $x+2y=3$.

Step-by-step solution

Step-1 – Apply the concept of slope-intercept form

Equation of line in slope intercept form is expressed below.

$y=mx+c$

Where m is the slope and c is the intercept of y-axis.

Step-2 –Write the equation in slope-intercept form

Consider the equation $4x+8y=12$.

Rewrite the equation in simplest form.

Divide both sides by 4.

$x+2y=3$

The equation resembles the equation in option C.

Also, convert the equation to slope-intercept form.

Subtract x from both the sides.

$\begin{array}{c}x+2y-x=3-x\\ 2y=3-x\end{array}$

Divide both sides by 2.

$\begin{array}{c}y=\frac{3}{2}-\frac{x}{2}\\ y=-\frac{1}{2}x+\frac{3}{2}\end{array}$

Step-3 – Graph the equations

Plot the equations.

The red line denotes the equation $x+2y=3$ and the equation $4x+8y=12$.

The equations are equivalent and the same line denote the graph of each equation.

Hence, the equation that has same graph as $4x+8y=12$ is $x+2y=3$.