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Algebra 1 : How to find the equation of a parallel line

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Example Question #21 : How To Find The Equation Of A Parallel Line

Which of the following lines is parallel to the following line:

$y=\frac{1}{2}x+2$ $\displaystyle y=\frac{1}{2}x+2$

Possible Answers:

y=-2x $\displaystyle y=-2x$

y=2x $\displaystyle y=2x$

y=x+2 $\displaystyle y=x+2$

$y=-\frac{1}{2}x$ $\displaystyle y=-\frac{1}{2}x$

$y=\frac{1}{2}x$ $\displaystyle y=\frac{1}{2}x$

Correct answer:

$y=\frac{1}{2}x$ $\displaystyle y=\frac{1}{2}x$

Explanation:

Parallel lines have the same slope and the only equation that has the same slope as the given equation is

$y=\frac{1}{2}x$ $\displaystyle y=\frac{1}{2}x$

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Example Question #21 : How To Find The Equation Of A Parallel Line

Which of the lines is parallel to 3x+9y=5 $\displaystyle 3x+9y=5$ ?

Possible Answers:

$x=-\frac{1}{3}$ $\displaystyle x=-\frac{1}{3}$

y=3x+2 $\displaystyle y=3x+2$

$y=-\frac{1}{3}x+2$ $\displaystyle y=-\frac{1}{3}x+2$

$x=-\frac{1}{3}y+2$ $\displaystyle x=-\frac{1}{3}y+2$

$y=-\frac{1}{3}$ $\displaystyle y=-\frac{1}{3}$

Correct answer:

$y=-\frac{1}{3}x+2$ $\displaystyle y=-\frac{1}{3}x+2$

Explanation:

In order for the lines to be parallel, both lines must have similar slope.

The current linear equation is in standard form. Rewrite this equation in slope intercept form, y=mx+b $\displaystyle y=mx+b$ .

The slope is represented by the $\displaystyle m$ in the equation.

Subtract $\displaystyle 3x$ on both sides.

$\displaystyle 3x+9y-3x=5-3x$

Simplify the left side and rearrange the right side.

$\displaystyle 9y=-3x+5$

Divide by nine on both sides.

$\frac{9y}{9}=\frac{-3x+5}{9}$ $\displaystyle \frac{9y}{9}=\frac{-3x+5}{9}$

Simplify both sides of the equation.

$y=-\frac{1}{3}x+\frac{5}{9}$ $\displaystyle y=-\frac{1}{3}x+\frac{5}{9}$

The slope of this line is $-\frac{1}{3}$ $\displaystyle -\frac{1}{3}$ .

The only line provided that has the similar slope is: $y=-\frac{1}{3}x+2$ $\displaystyle y=-\frac{1}{3}x+2$

The answer is: $y=-\frac{1}{3}x+2$ $\displaystyle y=-\frac{1}{3}x+2$

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Algebra 1 : How to find the equation of a parallel line

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #21 : How To Find The Equation Of A Parallel Line

Example Question #21 : How To Find The Equation Of A Parallel Line

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