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Intermediate Geometry : Coordinate Geometry

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Example Questions

Example Question #111 : Coordinate Geometry

Find the equation of a line passing through the points (0,-5) and (5,0) .

Possible Answers:

None of these.

y=-x-5

y=-x+5

y=x+5

y=x-5

Correct answer:

y=x-5

Explanation:

To find the equation of a line passing through these points we must find a line with that same slope. Start by finding the slope between the two points and then use the point slope equation to find the equation of the line.

slope:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{0--5}{5-0}=1$

Now use the point slope equation:

$y-y_{1}=m(x-x_{1})\rightarrow y-(-5)=1(x-0)\rightarrow \mathbf{y=x-5}$

*make sure you use the SAME coordinate pair when substituting x and y into the point slope equation.

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Example Question #112 : Lines

Find the equation of a line that goes through the points (3, 12) and (-2, 5) .

Possible Answers:

$y=-\frac{2}{5}x-\frac{11}{5}$

$y=-\frac{1}{6}x-\frac{6}{5}$

$y=\frac{7}{5}x+\frac{39}{5}$

$y=\frac{2}{3}x+\frac{4}{9}$

Correct answer:

$y=\frac{7}{5}x+\frac{39}{5}$

Explanation:

Recall that the slope-intercept form of a line:

y=mx+b ,

where $m=\text{slope}$ and $b=\text{y-intercept}$ .

First, find the slope of the line by using the following formula:

$\text{Slope of Line}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{5-12}{-2-3}=\frac{7}{5}$

Next, find the y-intercept of the line by plugging in of the points into the semi-completed formula.

$y=\frac{7}{5}x+b$

Plugging in (3, 12) yields the following:

$12=\frac{7}{5}(3)+b$

Solve for .

$b+\frac{21}{5}=12$

$b=\frac{39}{5}$

The equation of the line is then $y=\frac{7}{5}x+\frac{39}{5}$ .

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Example Question #113 : Lines

Find the equation of a line that goes through the points (-10, 7) and (12, 8)} .

Possible Answers:

$y=\frac{5}{18}x+\frac{1}{9}$

$y=\frac{1}{22}x+\frac{82}{11}$

$y=-\frac{18}{19}x-\frac{6}{19}$

y=22x+5

Correct answer:

$y=\frac{1}{22}x+\frac{82}{11}$

Explanation:

Recall that the slope-intercept form of a line:

y=mx+b ,

where $m=\text{slope}$ and $b=\text{y-intercept}$ .

First, find the slope of the line by using the following formula:

$\text{Slope of Line}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{8-7}{12-(-10)}=\frac{1}{22}$

Next, find the y-intercept of the line by plugging in of the points into the semi-completed formula.

$y=\frac{1}{22}x+b$

Plugging in (12, 8) yields the following:

$8=\frac{1}{22}(12)+b$

Solve for .

$b+\frac{6}{11}=8$

$b=\frac{82}{11}$

The equation of the line is then $y=\frac{1}{22}x+\frac{82}{11}$ .

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Example Question #1392 : Intermediate Geometry

Find the equation of a line that goes through the points (16, 10) and (15, 2) .

Possible Answers:

y=4x+108

$y=\frac{1}{8}x+112$

y=8x-118

$y=-\frac{1}{4}x-111$

Correct answer:

y=8x-118

Explanation:

Recall that the slope-intercept form of a line:

y=mx+b ,

where $m=\text{slope}$ and $b=\text{y-intercept}$ .

First, find the slope of the line by using the following formula:

$\text{Slope of Line}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{10-2}{16-15}=8$

Next, find the y-intercept of the line by plugging in of the points into the semi-completed formula.

y=8x+b

Plugging in (16, 10) yields the following:

10=8(16)+b

Solve for .

b+128=10

b=-118

The equation of the line is then y=8x-118 .

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Example Question #1393 : Intermediate Geometry

Find the equation of a line that goes through the points (-3, -5) and (-4, 8) .

Possible Answers:

$y=-\frac{2}{13}x-\frac{16}{13}$

y=-12x+32

y=-17x-29

y=-13x-44

Correct answer:

y=-13x-44

Explanation:

Recall that the slope-intercept form of a line:

y=mx+b ,

where $m=\text{slope}$ and $b=\text{y-intercept}$ .

First, find the slope of the line by using the following formula:

$\text{Slope of Line}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{8-(-5)}{-4-(-3)}=-13$

Next, find the y-intercept of the line by plugging in of the points into the semi-completed formula.

y=-13x+b

Plugging in (-3, -5) yields the following:

-5=-13(-3)+b

Solve for .

b+39=-5

b=-44

The equation of the line is then y=-13x-44 .

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Example Question #1401 : Intermediate Geometry

Find the equation of the line that goes through the points (12, 0) and (0, 16) .

Possible Answers:

y=4x+16

$y=\frac{3}{4}x-2$

$y=-\frac{3}{4}x+12$

$y=-\frac{4}{3}x+16$

Correct answer:

$y=-\frac{4}{3}x+16$

Explanation:

Recall that the slope-intercept form of a line:

y=mx+b ,

where $m=\text{slope}$ and $b=\text{y-intercept}$ .

First, find the slope of the line by using the following formula:

$\text{Slope of Line}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{0-16}{12-0}=-\frac{4}{3}$

The y-intercept is since that is given as one of the points on the line.

The line must have the equation $y=-\frac{4}{3}x+16$ .

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Example Question #1402 : Intermediate Geometry

Find the equation of the line that goes through the points (20, 18) and (-40, -36) .

Possible Answers:

y=-8x+12

$y=\frac{9}{10}x$

$y=\frac{10}{9}x+4$

$y=-\frac{9}{10}x-1$

Correct answer:

$y=\frac{9}{10}x$

Explanation:

Recall that the slope-intercept form of a line:

y=mx+b ,

where $m=\text{slope}$ and $b=\text{y-intercept}$ .

First, find the slope of the line by using the following formula:

$\text{Slope of Line}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{18-(-36)}{20-(-40)}=\frac{9}{10}$

Next, find the y-intercept of the line by plugging in of the points into the semi-completed formula.

$y=\frac{9}{10}x+b$

Plugging in (20, 18) yields the following:

$18=\frac{9}{10}(20)+b$

Solve for .

b+18=18

b=0

The equation of the line is then $y=\frac{9}{10}x$ .

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Example Question #1403 : Intermediate Geometry

Find the equation of the line that goes through the points (5, -10) and (15, 20) .

Possible Answers:

$y=-\frac{2}{3}x-9$

y=3x-25

$y=\frac{1}{3}x-10$

$y=\frac{3}{2}x+5$

Correct answer:

y=3x-25

Explanation:

Recall that the slope-intercept form of a line:

y=mx+b ,

where $m=\text{slope}$ and $b=\text{y-intercept}$ .

First, find the slope of the line by using the following formula:

$\text{Slope of Line}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{20-(-10)}{15-5}=3$

Next, find the y-intercept of the line by plugging in of the points into the semi-completed formula.

y=3x+b

Plugging in (5, -10) yields the following:

-10=3(5)+b

Solve for .

b+15=-10

b=-25

The equation of the line is then y=3x-25 .

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Example Question #1404 : Intermediate Geometry

Find the equation of the line that goes through the points (11, 2) and (11, 10) .

Possible Answers:

x=12y+2

y=11x-10

x=11

y=11

Correct answer:

x=11

Explanation:

Recall that the slope-intercept form of a line:

y=mx+b ,

where $m=\text{slope}$ and $b=\text{y-intercept}$ .

First, find the slope of the line by using the following formula:

$\text{Slope of Line}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{10-2}{11-11}=\text{Undefined}$

Since the slope of the line is undefined, this must be just a vertical line with the equation x=11 .

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Example Question #111 : Lines

Find the equation of the line that passes through the points (5, 7) and (-8, 7) .

Possible Answers:

$y=\frac{4}{5}x-\frac{3}{5}$

y=-x+14

y=7

$x=\frac{13}{2}$

Correct answer:

y=7

Explanation:

Recall that the slope-intercept form of a line:

y=mx+b ,

where $m=\text{slope}$ and $b=\text{y-intercept}$ .

First, find the slope of the line by using the following formula:

$\text{Slope of Line}=\frac{y_2-y_1}{x_2-x_1}$

$\text{Slope}=\frac{7-7}{5-(-8)}=0$

Since the slope is , the line is a horizontal line with the equation y=7 .

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Intermediate Geometry : Coordinate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #111 : Coordinate Geometry

Example Question #112 : Lines

Example Question #113 : Lines

Example Question #1392 : Intermediate Geometry

Example Question #1393 : Intermediate Geometry

Example Question #1401 : Intermediate Geometry

Example Question #1402 : Intermediate Geometry

Example Question #1403 : Intermediate Geometry

Example Question #1404 : Intermediate Geometry

Example Question #111 : Lines

All Intermediate Geometry Resources

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