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Intermediate Geometry : How to find out if a point is on a line with an equation

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #1361 : Intermediate Geometry

Which of the following points is on the line y=6x-5

Possible Answers:

(7,2)

(-3,4)

(2,7)

None of these

(-4,3)

Correct answer:

(2,7)

Explanation:

To ascertain if a point is on a line we must plug that coordinate pair into the equation of the line. If a true statement such as 5=5 is returned then we know that point is on our line.

y=6x-5

Choose the point you suspect is on the line.

(2,7)

7=6(2)-5

7=7

Since the equation returned a true statement the point $\mathbf{(2,7)}$ is on our line.

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Example Question #82 : Lines

Which of the following points is found on the line y=-2x+12 ?

Possible Answers:

(-20, 10)

(18, -26)

(12, -22)

(16, -20)

Correct answer:

(16, -20)

Explanation:

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.

Plugging in x=16 into the given equation will give the following:

y=-2x+12

y=-2(16)+12=-32+12=-20

Thus, (16, -20) is on the line.

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Example Question #83 : Lines

Which of the following points is found on the line $y=\frac{1}{6}x+5$ ?

Possible Answers:

(18, 2)

(12, -3)

(24, 9)

(60, 55)

Correct answer:

(24, 9)

Explanation:

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.

Plugging in x=24 into the given equation will give the following:

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

$y=\frac{1}{6}(24)+5=4+5=9$

Thus, (24, 9) is on the line.

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Example Question #84 : Lines

Which of the following points is found on the line y=-10x+8 ?

Possible Answers:

(5, -58)

(10, -92)

(-1, 2)

(20, 208)

Correct answer:

(10, -92)

Explanation:

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.

Plugging in x=10 into the given equation will give the following:

y=-10x+8

y=-10(10)+8=-100+8=-92

Thus, (10, -92) is on the line.

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Example Question #11 : Other Lines

Which of the following points is found on the line y=13x-11 ?

Possible Answers:

(2, 20)

(1, 2)

(13, 169)

(-10, 141)

Correct answer:

(1, 2)

Explanation:

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.

Plugging in x=1 into the given equation will give the following:

y=13x-11

y=13(1)-11=13-11=2

Thus, (1, 2) is on the line.

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Example Question #11 : Other Lines

Which of the following points is found on the line $y=-\frac{3}{2}x+10$ ?

Possible Answers:

(-8, 6)

(-10, 25)

(6, 19)

(12, 28)

Correct answer:

(-10, 25)

Explanation:

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.

Plugging in x=-10 into the given equation will give the following:

$y=-\frac{3}{2}x+10$

$y=-\frac{3}{2}(-10)+10=15+10=25$

Thus, (-10, 25) is on the line.

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Example Question #87 : Lines

Which of the following points is found on the line $y=\frac{1}{5}x-5$ ?

Possible Answers:

(12, 14)

$(-1, \frac{4}{5})$

(-20, -9)

$(2, -\frac{4}{5})$

Correct answer:

(-20, -9)

Explanation:

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.

Plugging in x=-20 into the given equation will give the following:

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

$y=\frac{1}{5}(-20)-5=-4-5=-9$

Thus, (-20, -9) is on the line.

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Example Question #88 : Lines

Which of the following points is found on the line 3x+4y=5 ?

Possible Answers:

(-1, 12)

$(2, -\frac{1}{2})$

$(12, -\frac{31}{4})$

$(0, -\frac{3}{4})$

Correct answer:

$(12, -\frac{31}{4})$

Explanation:

Start by rewriting the equation into slope-intercept form.

3x+4y=5

4y=-3x+5

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

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.

Plugging in x=12 into the given equation will give the following:

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

$y=-\frac{3}{4}(12)+\frac{5}{4}=-9+\frac{5}{4}=-\frac{31}{4}$

Thus, $(12, -\frac{31}{4})$ is on the line.

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Example Question #11 : Other Lines

Which of the following points is on the line 12x-4y=18 ?

Possible Answers:

$(-13, -\frac{87}{2})$

$(-\frac{1}{2}, 6)$

$(14, \frac{41}{2})$

$(\frac{3}{2}, 1)$

Correct answer:

$(-13, -\frac{87}{2})$

Explanation:

Start by rewriting the equation into slope-intercept form.

12x-4y=18

-4y=-12x+18

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

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.

Plugging in x=-13 into the given equation will give the following:

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

$y=3(-13)-\frac{9}{2}=-39-\frac{9}{2}=-\frac{87}{2}$

Thus, $(-13, -\frac{87}{2})$ is on the line.

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Example Question #91 : Lines

Which of the following points is found on the line 5y+10x=20 ?

Possible Answers:

$(\frac{1}{2}, -3)$

(-7, 18)

(8, 12)

(10, 9)

Correct answer:

(-7, 18)

Explanation:

Start by rewriting the equation into slope-intercept form.

5y+10x=20

5y=-10x+20

y=-2x+4

To find which point is on the line, take the -coordinate, and plug it into the given equation to solve for . If the -value matches the -coordinate of the same point, then the point is on the line.

Plugging in x=-7 into the given equation will give the following:

y=-2x+4

y=-2(-7)+4=18

Thus, (-7, 18) is on the line.

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Intermediate Geometry : How to find out if a point is on a line with an equation

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1361 : Intermediate Geometry

Example Question #82 : Lines

Example Question #83 : Lines

Example Question #84 : Lines

Example Question #11 : Other Lines

Example Question #11 : Other Lines

Example Question #87 : Lines

Example Question #88 : Lines

Example Question #11 : Other Lines

Example Question #91 : Lines

All Intermediate Geometry Resources

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