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Chapter 3: Q51. (page 115)

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

Expert verified

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

Step by step solution

01

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.

02

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.

x+2y鈭�x=3鈭�x2y=3鈭�x

Divide both sides by 2.

y=32鈭�x2y=鈭�12x+32

03

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.

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Most popular questions from this chapter

Graph each system of equations and describe it as consistent and independent, consistent and dependent, or inconsistent.
3x+y=36x+2y=6

Solve each system of equations by graphing.

14x+2y=52x鈭�y=6

Solve each system of equations.

x+y+z=鈭�12x+4y+z=1x+2y鈭�3z=鈭�3

58b+12=-34

The integer k is greater than 50 and less than 100. When k is divided by 3, the remainder is 1. When k is divided by 8, the remainder is 2. What is one possible value of k?
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