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GRE Subject Test: Math : Finding Equations of Lines

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Example Questions

Example Question #1 : Finding Equations Of Lines

What is the equation of the line (in slope-intercept form) that goes through the points: (2,4) and (7,8) ?

Possible Answers:

$y=-\frac {4}{5}x-\frac {12}{5}$

$y=-\frac {4}{5}x+\frac {12}{5}$

$y=\frac {4}{5}x+\frac {12}{5}$

$y=\frac {4}{5}x-\frac {12}{5}$

Correct answer:

$y=\frac {4}{5}x+\frac {12}{5}$

Explanation:

Step 1: Find the slope between the two points:

$\frac {y_2-y_1}{x_2-x_1}=\frac {8-4}{7-2}=\frac {4}{5}$

Step 2: Write the slope-intercept form:

$y=\frac {4}{5}x+b$

Step 3. Find b. Plug in (x,y) from one of the points:

$4=\frac {4}{5}(2)+b$

$4=\frac {8}{5}+b$

$4-\frac {8}{5}=b$

$\frac {20-8}{5}=b$

$\frac {12}{5}=b$
Step 4: Write out the full equation:

$y=\frac {4}{5}x+\frac {12}{5}$

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Example Question #1 : Finding Equations Of Lines

What is the equation of a line that passes through points (3,4) and (1,-2) in slope-intercept form?

Possible Answers:

y = 3x-13

y = 3x+13

y = 3x-5

y = 3x+5

Correct answer:

y = 3x-5

Explanation:

To find the equation of the line, first find the slope using the formula:

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

The points that the line passes through are (3,4) and (1,-2) .

$m = \frac{-2-4}{1-3}$

$m= \frac{-6}{-2}$

m = 3

Then pick one set of points and place in the form y = mx+b . Either set of points will give you the same equation. Points (3,4) were used.

$4 = 3\times 3 + b$

4 = 9 +b

Subtract from both sides of the equation.

4-9 = 9-9 +b

-5 = b

The equation of the line in slope-intercept form or is

y= 3x-5

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Example Question #61 : Functions And Graphs

Find the equation of a line in slope-intercept form that passes though points (-1,3) and (-2,5) .

Possible Answers:

y = -2x + 1

y = -2x - 1

y = 2x -1

y = 2x + 1

Correct answer:

y = -2x + 1

Explanation:

To find the equation of a line that passes through (-1,3) and (-2,5) , first find the slope using this formula:

$m = \frac{y_{2} -y_{1}}{x_{2}-x_{1}}$

$m = \frac{5-3}{-2-(-1)} = \frac{2}{-1}$

m = -2

Using one set of points or coordinates and the value of slope, plug these values into:

y=mx+b

Either set of points will give you the same equation of the line.

Coordinates (-1,3) .

y-3 = -2(x - (-1)

y-3 = -2(x+1)

Distribute the to what is inside the parenthesis.

$-2\times x = -2x$

$-2 \times 1 = -2$

y-3 = -2x-2

Add to both sides of the equation.

y-3+3 = -2x-2+3

The equation of the line in slope-intercept form y=mx+b is:

y = -2x +1

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Example Question #1 : Finding Equations Of Lines

A line has a slope of $m=-\frac{1}{4},$ and goes through point (0,8). What is the equation of the line in slope-intercept form?

Possible Answers:

$y = -\frac{1}{4} -8$

$y = \frac{1}{4} +8$

$y = \frac{1}{4} - 8$

$y = -\frac{1}{4} +8$

Correct answer:

$y = -\frac{1}{4} +8$

Explanation:

The slope-intercept form is y = mx+b , where represents the slope, and represent the points, and is the y-intercept or the value of when x=0.

The slope or $\frac{rise}{run}$ has been given as $m=-\frac{1}{4}$ .

The points that this equation of the line passes through are (0,8) and

b=8 because based on the points, when x=0,y=8. That is the y-intercept.

The equation of the line in slope-intercept form y=mx+b is:

$y=-\frac{1}{4} x+8$

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Example Question #2 : Finding Equations Of Lines

Find the equation of a line in slope-intercept form that passes through points (-5,-3) and has a slope of m=-2.

Possible Answers:

y = -2x-13

y = 2x+13

y = 2x-13

y = -2x+13

Correct answer:

y = -2x-13

Explanation:

To find the equation of a line given points (-5, -3) and m = -2, use the point- slope formula:

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

y -(-3) = -2 (x--5)

y +3 = -2(x+5)

Distribute the to what is inside the parenthesis.

-2(x) = -2x

$-2\times 5 = -10$

y + 3 = -2x-10

Subtract from both sides of the equation.

y+3-3 = -2x-10-3

-10-3 = -13 When the sign is the same for both integers, add.

The equation of the line in slope-intercept form y=mx+b is:

y=-2x-13

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Example Question #43 : Coordinate Geometry

Find the equation of the line with points (1,6) (3, -2)

Possible Answers:

y=10x-4

y=1/4-10

y=4-25/4

y=-4x+10

y=-1/4x+25/4

Correct answer:

y=-4x+10

Explanation:

y=mx+b

To solve for you must use the equation $(y^{1}-y^{2})/(x^{1}-x^{2})$

(6-(-2))/(1-3) = -8/2 = -4

y=-4x+b

To solve for be we must plug in one of the points

6=-4(1)+b

simplify

6=-4+b

Add to both sides

10=b

y=-4x+10

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Example Question #2 : Finding Equations Of Lines

Find a line through the point (2,3) perpendicular to the line 4x+y=7 .

Possible Answers:

y=4x+5/2

y=4x+7

y=1/4x+5/2

y=1/4x+7

7=-4x+5/2

Correct answer:

y=1/4x+5/2

Explanation:

To solve this problem you must first find the slope of the original equation by point it into y-mx+b form

4x+y=7

subtract x from both sides

y=-4x+7

Then you must find the reciprocal of the slope to get the slope of the perpendicular line

reciprocal is 1/4

Finally you must you point-slope form to solve

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

y-(3)=1/4(x-(2))

Multiply 1/4 through the parentheses

y-3=1/4x-1/2

add three to both sides

y=1/4x+5/2

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GRE Subject Test: Math : Finding Equations of Lines

Study concepts, example questions & explanations for GRE Subject Test: Math

All GRE Subject Test: Math Resources

Example Questions

Example Question #1 : Finding Equations Of Lines

Example Question #1 : Finding Equations Of Lines

Example Question #61 : Functions And Graphs

Example Question #1 : Finding Equations Of Lines

Example Question #2 : Finding Equations Of Lines

Example Question #43 : Coordinate Geometry

Example Question #2 : Finding Equations Of Lines

All GRE Subject Test: Math Resources

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