Calculating the equation of a parallel line - GMAT Quantitative Reasoning

Card 0 of 7

Question

Find the equation of a line that is parallel to and passes through the point .

Answer

The parallel line has the equation $\dpi{100} \small 4x-2y=5$ . We can find the slope by putting the equation into slope-intercept form, y = mx + b, where m is the slope and b is the intercept. $\dpi{100} \small 4x-2y=5$ becomes $\dpi{100} \small y=2x-\frac{5}{2}$ , so the slope is 2.

We know that our line must have an equation that looks like $\dpi{100} \small y=2x+b$ . Now we need the intercept. We can solve for b by plugging in the point (4, 1).

1 = 2(4) + b

b = –7

Then the line in question is $\dpi{100} \small y=2x-7$ .

Compare your answer with the correct one above

Question

What is the equation of the line that is parallel to and goes through point ?

Answer

Parallel lines have the same slope. Therefore, the slope of the new line is , as the equation of the original line is ,with slope .

and :

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

Compare your answer with the correct one above

Question

Given:

$\small f(x)=4x+13$

Which of the following is the equation of a line parallel to that has a y-intercept of ?

Answer

Parallel lines have the same slope, so our slope will still be 4. The y-intercept is just the "+b" at the end. In f(x) the y-intercept is 13. In this case, we need to have a y-intercept of -13, so our equation just becomes:

$\small \small f(x)=4x-13$

Compare your answer with the correct one above

Question

Find the equation of the line that is parallel to the and passes through the point .

$\small g(x)=6x+7$

Answer

Two lines are parallel if they have the same slope. The slope of g(x) is 6, so eliminate anything without a slope of 6.

Recall slope intercept form which is .

We know that the line must have an m of 6 and an (x,y) of (8,9). Plug everything in and go from there.

$9=(6\cdot 8)+b$

$\small 9=48+b$

$\small b=9-48=-39$

So we get:

$\small y=6x-39$

Compare your answer with the correct one above

Question

Given the function , which of the following is the equation of a line parallel to and has a -intercept of ?

Answer

Given a line defined by the equation with slope , any line that is parallel to also has a slope of . Since , the slope is and the slope of any line parallel to also has a slope of .

Since also needs to have a -intercept of , then the equation for must be .

Compare your answer with the correct one above

Question

Given the function $f(x)=-\frac{6}{5}x+7$ , which of the following is the equation of a line parallel to and has a -intercept of ?

Answer

Given a line defined by the equation with slope , any line that is parallel to also has a slope of . Since $f(x)=-\frac{6}{5}x+7$ , the slope is $-\frac{6}{5}$ and the slope of any line parallel to also has a slope of $m=-\frac{6}{5}$ .

Since also needs to have a -intercept of , then the equation for must be $g(x)=-\frac{6}{5}x-2$ .

Compare your answer with the correct one above

Question

Given the function , which of the following is the equation of a line parallel to and has a -intercept of ?

Answer

Given a line defined by the equation with slope , any line that is parallel to also has a slope of . Since , the slope is and the slope of any line parallel to also has a slope of .

Since also needs to have a -intercept of , then the equation for must be .

Compare your answer with the correct one above

Tap the card to reveal the answer