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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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8 Diagnostic Tests 250 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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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Example Question #121 : Lines

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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Example Question #25 : How To Find The Equation Of A Line

Find the equation of the line that passes through the points (-17, 1) and (-1, 10) .

Possible Answers:

$y=\frac{9}{4}x+\frac{107}{4}$

$y=\frac{16}{9}x+\frac{100}{9}$

$y=\frac{9}{16}x+\frac{169}{16}$

$y=-\frac{9}{16}x+\frac{3}{16}$

Correct answer:

$y=\frac{9}{16}x+\frac{169}{16}$

Explanation:

Start by finding the slope of the line.

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

$\text{Slope}=\frac{10-1}{-1-(-17)}=\frac{9}{16}$

Now, take one of the points and put the equation into point-slope form. Recall the point-slope form of an equation of a line:

y-y_1=m(x-x_1) , where is the slope and (x_1, y_1) is the point.

$y-10=\frac{9}{16}(x+1)$

Now, simplify this equation so that it is in slope-intercept form. Recall the slope-intercept form of an equation of a line:

y=mx+b , where is the slope and is the y-intercept.

$y-10=\frac{9}{16}(x+1)$

$y-10=\frac{9}{16}x+\frac{9}{16}$

$y=\frac{9}{16}x+\frac{169}{16}$

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Example Question #26 : How To Find The Equation Of A Line

Find the equation of a line that passes through the points (4, 12) and (12, 10) .

Possible Answers:

$y=\frac{1}{4}x+16$

$y=-\frac{1}{4}x+13$

y=4x+10

y=-4x+8

Correct answer:

$y=-\frac{1}{4}x+13$

Explanation:

Start by finding the slope of the line.

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

$\text{Slope}=\frac{10-12}{12-4}=-\frac{1}{4}$

Now, take one of the points and put the equation into point-slope form. Recall the point-slope form of an equation of a line:

y-y_1=m(x-x_1) , where is the slope and (x_1, y_1) is the point.

$y-12=-\frac{1}{4}(x-4)$

Now, simplify this equation so that it is in slope-intercept form. Recall the slope-intercept form of an equation of a line:

y=mx+b , where is the slope and is the y-intercept.

$y-12=-\frac{1}{4}(x-4)$

$y-12=-\frac{1}{4}x+1$

$y=-\frac{1}{4}x+13$

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Example Question #1401 : Intermediate Geometry

Find the equation of the line that passes through the points $(-\frac{1}{2}, 6)$ and $(\frac{3}{2}, 7)$ .

Possible Answers:

$y=\frac{1}{2}x+\frac{21}{2}$

$y=\frac{1}{2}x+\frac{9}{2}$

$y=\frac{1}{2}x+\frac{25}{4}$

$y=\frac{1}{2}x+\frac{19}{4}$

Correct answer:

$y=\frac{1}{2}x+\frac{25}{4}$

Explanation:

Start by finding the slope of the line.

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

$\text{Slope}=\frac{7-6}{\frac{3}{2}-(-\frac{1}{2})}=\frac{1}{2}$

Now, take one of the points and put the equation into point-slope form. Recall the point-slope form of an equation of a line:

y-y_1=m(x-x_1) , where is the slope and (x_1, y_1) is the point.

$y-7=\frac{1}{2}(x-\frac{3}{2})$

Now, simplify this equation so that it is in slope-intercept form. Recall the slope-intercept form of an equation of a line:

y=mx+b , where is the slope and is the y-intercept.

$y-7=\frac{1}{2}(x-\frac{3}{2})$

$y-7=\frac{1}{2}x-\frac{3}{4}$

$y-7=\frac{1}{2}x+\frac{25}{4}$

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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1401 : Intermediate Geometry

Example Question #1402 : Intermediate Geometry

Example Question #1403 : Intermediate Geometry

Example Question #1404 : Intermediate Geometry

Example Question #111 : Lines

Example Question #121 : Lines

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

Example Question #25 : How To Find The Equation Of A Line

Example Question #26 : How To Find The Equation Of A Line

Example Question #1401 : Intermediate Geometry

All Intermediate Geometry Resources

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