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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #1531 : Intermediate Geometry

Find the x-intercept for the line 12x-2y=2 .

Possible Answers:

(6, 0)

$(\frac{1}{6}, 0)$

$(\frac{1}{3}, 0)$

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

Correct answer:

$(\frac{1}{6}, 0)$

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

12x-2y=2

2y+2=12x

2y=12x-2

y=6x-1

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

0=6x-1

Now, solve for .

6x=1

$x=\frac{1}{6}$

The x-intercept is found at $(\frac{1}{6}, 0)$ .

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Example Question #1532 : Intermediate Geometry

Find the x-intercept for the line 10y-5x=25 .

Possible Answers:

$(\frac{1}{5}, 0)$

(-5, 0)

$(\frac{3}{5}, 0)$

$(-\frac{5}{2}, 0)$

Correct answer:

(-5, 0)

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

10y-5x=25

10y=5x+25

$y=\frac{1}{2}x+\frac{5}{2}$

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

$0=\frac{1}{2}x+\frac{5}{2}$

Now, solve for .

$\frac{1}{2}x=-\frac{5}{2}$

x=-5

The x-intercept is found at (-5, 0) .

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Example Question #1533 : Intermediate Geometry

Find the x-intercept for the line 5x-2y=4 .

Possible Answers:

$(-\frac{5}{4}, 0)$

$(\frac{4}{5}, 0)$

$(\frac{5}{2}, 0)$

$(\frac{3}{5}, 0)$

Correct answer:

$(\frac{4}{5}, 0)$

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

5x-2y=4

2y+4=5x

2y=5x-4

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

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

$0=\frac{5}{2}x-2$

Now, solve for .

$\frac{5}{2}x=2$

$x=\frac{4}{5}$

The x-intercept is found at $(\frac{4}{5}, 0)$ .

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Example Question #1534 : Intermediate Geometry

Find the x-intercept of the line 3y-6x=21 .

Possible Answers:

$(-\frac{7}{2}, 0)$

$(\frac{5}{2}, 0)$

$(\frac{3}{7}, 0)$

(-4, 0)

Correct answer:

$(-\frac{7}{2}, 0)$

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

3y-6x=21

3y=6x+21

y=2x+7

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

0=2x+7

Now, solve for .

2x=-7

$x=-\frac{7}{2}$

The x-intercept is found at $(-\frac{7}{2}, 0)$ .

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Example Question #1535 : Intermediate Geometry

Find the x-intercept of the line 12x-15y=-6 .

Possible Answers:

$(-\frac{3}{2}, 0)$

(-3, 0)

$(-\frac{1}{2},0)$

(-2, 0)

Correct answer:

$(-\frac{1}{2},0)$

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

12x-15y=-6

15y-6=12x

15y=12x+6

$y=\frac{4}{5}x+\frac{2}{5}$

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

$0=\frac{4}{5}x+\frac{2}{5}$

Now, solve for .

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

$x=-\frac{1}{2}$

The x-intercept is found at $(-\frac{1}{2}, 0)$ .

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Example Question #1536 : Intermediate Geometry

Find the x-intercept of the line 19x+5y=2 .

Possible Answers:

$(-\frac{19}{2},0)$

$(\frac{2}{19},0)$

$(-\frac{15}{19},0)$

$(\frac{5}{19},0)$

Correct answer:

$(\frac{2}{19},0)$

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

19x+5y=2

5y=-19x+2

$y=-\frac{19}{5}x+\frac{2}{5}$

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

$0=-\frac{19}{5}x+\frac{2}{5}$

Now, solve for .

$\frac{19}{5}x=\frac{2}{5}$

$x=\frac{2}{19}$

The x-intercept is found at $(\frac{2}{19}, 0)$ .

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Example Question #1537 : Intermediate Geometry

Find the x-intercept for the line 8x-9y=12 .

Possible Answers:

(2, 0)

$(\frac{3}{2},0)$

$(-\frac{1}{2},0)$

$(-\frac{2}{3},0)$

Correct answer:

$(\frac{3}{2},0)$

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

8x-9y=12

9y+12=8x

9y=8x-12

$y=\frac{8}{9}x-\frac{4}{3}$

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

$0=\frac{8}{9}x-\frac{4}{3}$

Now, solve for .

$\frac{8}{9}x=\frac{4}{3}$

$x=\frac{3}{2}$

The x-intercept is found at $(\frac{3}{2}, 0)$ .

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Example Question #1538 : Intermediate Geometry

Find the x-intercept for the line -8x+2y=1 .

Possible Answers:

$(-\frac{1}{2},0)$

$(-\frac{1}{4},0)$

$(-\frac{1}{8},0)$

$(-\frac{3}{8},0)$

Correct answer:

$(-\frac{1}{8},0)$

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

-8x+2y=1

2y=8x+1

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

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

$0=4x+\frac{1}{2}$

Now, solve for .

$4x=-\frac{1}{2}$

$x=-\frac{1}{8}$

The x-intercept is found at $(-\frac{1}{8}, 0)$ .

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Example Question #1539 : Intermediate Geometry

Find the x-intercept of the line -5x-6y=23 .

Possible Answers:

$(-\frac{12}{5},0)$

$(-\frac{17}{5},0)$

$(-\frac{23}{5},0)$

$(-\frac{115}{36},0)$

Correct answer:

$(-\frac{23}{5},0)$

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

-5x-6y=23

6y+23=-5x

6y=-5x-23

$y=-\frac{5}{6}x-\frac{23}{6}$

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

$0=-\frac{5}{6}x-\frac{23}{6}$

Now, solve for .

$\frac{5}{6}x=-\frac{23}{6}$

$x=-\frac{23}{5}$

The x-intercept is found at $(-\frac{23}{5}, 0)$ .

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Example Question #1540 : Intermediate Geometry

Find the x-intercept for the line 4x-9y=15 .

Possible Answers:

(4, 0)

$(\frac{15}{4}, 0)$

(3, 0)

$(\frac{17}{4},0)$

Correct answer:

$(\frac{15}{4}, 0)$

Explanation:

Start by putting the equation into y=mx+b form, where is the slope, and is the y-intercept.

4x-9y=15

15+9y=4x

9y=4x-15

$y=\frac{4}{9}x-\frac{5}{3}$

By definition, the x-intercept is where the line crosses the x-axis. As such, the y-coordinate of this point must be .

Plug in for in the equation for this line.

$0=\frac{4}{9}x-\frac{5}{3}$

Now, solve for .

$\frac{4}{9}x=\frac{5}{3}$

$x=\frac{15}{4}$

The x-intercept is found at $(\frac{15}{4}, 0)$ .

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Intermediate Geometry : Intermediate Geometry

Study concepts, example questions & explanations for Intermediate Geometry

All Intermediate Geometry Resources

Example Questions

Example Question #1531 : Intermediate Geometry

Example Question #1532 : Intermediate Geometry

Example Question #1533 : Intermediate Geometry

Example Question #1534 : Intermediate Geometry

Example Question #1535 : Intermediate Geometry

Example Question #1536 : Intermediate Geometry

Example Question #1537 : Intermediate Geometry

Example Question #1538 : Intermediate Geometry

Example Question #1539 : Intermediate Geometry

Example Question #1540 : Intermediate Geometry

All Intermediate Geometry Resources

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