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Intermediate Geometry : Other Lines

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Example Questions

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Example Question #41 : Other Lines

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

Possible Answers:

y=22x+5

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

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

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

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 #42 : Other Lines

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

Possible Answers:

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

y=8x-118

y=4x+108

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

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 #43 : Other Lines

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

Possible Answers:

y=-12x+32

y=-13x-44

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

y=-17x-29

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 #44 : Other Lines

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

Possible Answers:

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

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

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

y=4x+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 #45 : Other Lines

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

Possible Answers:

y=-8x+12

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

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

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

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 #46 : Other Lines

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

Possible Answers:

y=3x-25

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

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

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

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 #21 : How To Find The Equation Of A Line

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

Possible Answers:

y=11x-10

x=12y+2

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 #22 : How To Find The Equation Of A Line

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

Possible Answers:

y=7

y=-x+14

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

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

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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Example Question #1401 : Intermediate Geometry

Find the equation of the line that passes through the points (14, 9) and (-6, 12) .

Possible Answers:

$y=-\frac{15}{26}x-\frac{111}{26}$

$y=\frac{3}{26}x-\frac{113}{13}$

$y=\frac{20}{3}x+\frac{120}{11}$

$y=-\frac{3}{20}x+\frac{111}{10}$

Correct answer:

$y=-\frac{3}{20}x+\frac{111}{10}$

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:

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

$\text{Slope}=\frac{12-9}{-6-14}=-\frac{3}{20}$

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

$y=-\frac{3}{20}x+b$

Plugging in (14, 9) yields the following:

$9=-\frac{3}{20}(14)+b$

Solve for .

$b-\frac{21}{10}=9$

$b=\frac{111}{10}$

The equation of the line is then $y=-\frac{3}{20}x+\frac{111}{10}$ .

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Example Question #24 : How To Find The Equation Of A Line

Find the equation of the line that passes through the points (20, -3) and (-45, 6) .

Possible Answers:

$y=-\frac{9}{65}x-\frac{3}{13}$

$y=-\frac{13}{24}x-\frac{1}{12}$

$y=-\frac{24}{13}x+\frac{4}{13}$

$y=-\frac{65}{4}x-\frac{5}{2}$

Correct answer:

$y=-\frac{9}{65}x-\frac{3}{13}$

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:

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

$\text{Slope}=\frac{6-(-3)}{-45-20}=-\frac{9}{65}$

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

$y=-\frac{9}{65}x+b$

Plugging in (20, -3) yields the following:

$-3=-\frac{9}{65}(20)+b$

Solve for .

$b-\frac{36}{13}=-3$

$b=-\frac{3}{13}$

The equation of the line is then $y=-\frac{9}{65}x-\frac{3}{13}$ .

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Intermediate Geometry : Other Lines

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #41 : Other Lines

Example Question #42 : Other Lines

Example Question #43 : Other Lines

Example Question #44 : Other Lines

Example Question #45 : Other Lines

Example Question #46 : Other Lines

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

Example Question #22 : How To Find The Equation Of A Line

Example Question #1401 : Intermediate Geometry

Example Question #24 : How To Find The Equation Of A Line

All Intermediate Geometry Resources

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