How to find the equation of a parallel line - Math

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Question

What line is parallel to through the point ?

Answer

The given line can be rewritten as $y=-\frac{1}{2}x+\frac{7}{10}$ , which has slope $m=-\frac{1}{2}$ .

If the new line is parallel to the old line, it must have the same slope. So we use the point-slope form of an equation to calculate the new intercept.

becomes $7=-\frac{1}{2}(-6)+b$ where .

So the equation of the parallel line is $y=-\frac{1}{2}x+4$ .

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Question

Find the equation of a line parallel to the line that goes through points $\left ( 2,4 \right )$ and $\left ( 0,7 \right )$ .

Answer

Parallel lines share the same slope. Because the slope of the original line is $-\frac{3}{2}$ , the correct answer must have that slope, so the correct answer is

$y=-\frac{3}{2}X+7$

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Question

Find the equation of a line parallel to .

Answer

Since parallel lines share the same slope, the only answer that works is

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Question

Given the equation and the point , find a line through the point that is parallel to the given line.

Answer

In order for two lines to be parallel, they must have the same slope. The slope of the given line is , so we know that the line going through the given point also has to have a slope of . Using the point-slope formula,

$y-y_{1}=m(x-x_1)$ ,

where represents the slope and and represent the given points, plug in the points given and simplify into standard form:

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Question

What line is parallel to through ?

Answer

Parallel lines have the same slopes. The slope for the given equation is . We can use the slope and the new point in the slope intercept equation to solve for the intercept:

Therefore the new equation becomes:

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Question

What line is parallel to $y=\frac{1}{2}x-2$ through ?

Answer

Parallel lines have the same slope. The slope of the given line is $\frac{1}{2}$ .

Find the line with slope $\frac{1}{2}$ through the point by plugging this informatuon into the slope intercept equation, :

$7=\frac{1}{2}(6)+b$ , which gives .

Solve for by subtracting from both sides to get .

Then the parallel line equation becomes $y=\frac{1}{2}x+4$ , and converting to standard form gives .

Compare your answer with the correct one above

Question

What line is parallel to through the point ?

Answer

The given line can be rewritten as $y=-\frac{1}{2}x+\frac{7}{10}$ , which has slope $m=-\frac{1}{2}$ .

If the new line is parallel to the old line, it must have the same slope. So we use the point-slope form of an equation to calculate the new intercept.

becomes $7=-\frac{1}{2}(-6)+b$ where .

So the equation of the parallel line is $y=-\frac{1}{2}x+4$ .

Compare your answer with the correct one above

Question

Find the equation of a line parallel to the line that goes through points $\left ( 2,4 \right )$ and $\left ( 0,7 \right )$ .

Answer

Parallel lines share the same slope. Because the slope of the original line is $-\frac{3}{2}$ , the correct answer must have that slope, so the correct answer is

$y=-\frac{3}{2}X+7$

Compare your answer with the correct one above

Question

Find the equation of a line parallel to .

Answer

Since parallel lines share the same slope, the only answer that works is

Compare your answer with the correct one above

Question

Given the equation and the point , find a line through the point that is parallel to the given line.

Answer

In order for two lines to be parallel, they must have the same slope. The slope of the given line is , so we know that the line going through the given point also has to have a slope of . Using the point-slope formula,

$y-y_{1}=m(x-x_1)$ ,

where represents the slope and and represent the given points, plug in the points given and simplify into standard form:

Compare your answer with the correct one above

Question

What line is parallel to through ?

Answer

Parallel lines have the same slopes. The slope for the given equation is . We can use the slope and the new point in the slope intercept equation to solve for the intercept:

Therefore the new equation becomes:

Compare your answer with the correct one above

Question

What line is parallel to $y=\frac{1}{2}x-2$ through ?

Answer

Parallel lines have the same slope. The slope of the given line is $\frac{1}{2}$ .

Find the line with slope $\frac{1}{2}$ through the point by plugging this informatuon into the slope intercept equation, :

$7=\frac{1}{2}(6)+b$ , which gives .

Solve for by subtracting from both sides to get .

Then the parallel line equation becomes $y=\frac{1}{2}x+4$ , and converting to standard form gives .

Compare your answer with the correct one above

Question

What line is parallel to through the point ?

Answer

The given line can be rewritten as $y=-\frac{1}{2}x+\frac{7}{10}$ , which has slope $m=-\frac{1}{2}$ .

If the new line is parallel to the old line, it must have the same slope. So we use the point-slope form of an equation to calculate the new intercept.

becomes $7=-\frac{1}{2}(-6)+b$ where .

So the equation of the parallel line is $y=-\frac{1}{2}x+4$ .

Compare your answer with the correct one above

Question

Find the equation of a line parallel to the line that goes through points $\left ( 2,4 \right )$ and $\left ( 0,7 \right )$ .

Answer

Parallel lines share the same slope. Because the slope of the original line is $-\frac{3}{2}$ , the correct answer must have that slope, so the correct answer is

$y=-\frac{3}{2}X+7$

Compare your answer with the correct one above

Question

Find the equation of a line parallel to .

Answer

Since parallel lines share the same slope, the only answer that works is

Compare your answer with the correct one above

Question

Given the equation and the point , find a line through the point that is parallel to the given line.

Answer

In order for two lines to be parallel, they must have the same slope. The slope of the given line is , so we know that the line going through the given point also has to have a slope of . Using the point-slope formula,

$y-y_{1}=m(x-x_1)$ ,

where represents the slope and and represent the given points, plug in the points given and simplify into standard form:

Compare your answer with the correct one above

Question

What line is parallel to through ?

Answer

Parallel lines have the same slopes. The slope for the given equation is . We can use the slope and the new point in the slope intercept equation to solve for the intercept:

Therefore the new equation becomes:

Compare your answer with the correct one above

Question

What line is parallel to $y=\frac{1}{2}x-2$ through ?

Answer

Parallel lines have the same slope. The slope of the given line is $\frac{1}{2}$ .

Find the line with slope $\frac{1}{2}$ through the point by plugging this informatuon into the slope intercept equation, :

$7=\frac{1}{2}(6)+b$ , which gives .

Solve for by subtracting from both sides to get .

Then the parallel line equation becomes $y=\frac{1}{2}x+4$ , and converting to standard form gives .

Compare your answer with the correct one above

Question

What line is parallel to through the point ?

Answer

The given line can be rewritten as $y=-\frac{1}{2}x+\frac{7}{10}$ , which has slope $m=-\frac{1}{2}$ .

If the new line is parallel to the old line, it must have the same slope. So we use the point-slope form of an equation to calculate the new intercept.

becomes $7=-\frac{1}{2}(-6)+b$ where .

So the equation of the parallel line is $y=-\frac{1}{2}x+4$ .

Compare your answer with the correct one above

Question

Find the equation of a line parallel to the line that goes through points $\left ( 2,4 \right )$ and $\left ( 0,7 \right )$ .

Answer

Parallel lines share the same slope. Because the slope of the original line is $-\frac{3}{2}$ , the correct answer must have that slope, so the correct answer is

$y=-\frac{3}{2}X+7$

Compare your answer with the correct one above

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