Chapter 3: Q51. (page 115)

Which equation has the same graph as $4 x + 8 y = 12$ ?
$\begin{matrix} A. x + y = 3 \\ B. 2 x + y = 3 \\ C. x + 2 y = 3 \\ D. 2 x + 2 y = 6 \end{matrix}$

Short Answer

Expert verified

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

Step by step solution

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

Equation of line in slope intercept form is expressed below.

$y = m x + c$

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 $4 x + 8 y = 12$ .

Rewrite the equation in simplest form.

Divide both sides by 4.

$x + 2 y = 3$

The equation resembles the equation in option C.

Also, convert the equation to slope-intercept form.

Subtract x from both the sides.

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

Divide both sides by 2.

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

Step-3 – Graph the equations

Plot the equations.

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

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

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

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Which equation has the same graph as $4 x + 8 y = 12$ ?
$\begin{matrix} A. x + y = 3 \\ B. 2 x + y = 3 \\ C. x + 2 y = 3 \\ D. 2 x + 2 y = 6 \end{matrix}$

Short Answer

Step by step solution

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

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

Step-3 – Graph the equations

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Which equation has the same graph as 4x+8y=12?A.x+y=3B.2x+y=3C.x+2y=3D.2x+2y=6

Short Answer

Step by step solution

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

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

Step-3 – Graph the equations

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Decision Maths

Pure Maths

Geometry

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Which equation has the same graph as $4 x + 8 y = 12$ ?
$\begin{matrix} A. x + y = 3 \\ B. 2 x + y = 3 \\ C. x + 2 y = 3 \\ D. 2 x + 2 y = 6 \end{matrix}$