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High School Math : Algebra I

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Example Questions

Example Question #1 : How To Find The Equation Of A Parallel Line

What line is parallel to 5x + 10y=7 through the point (-6,7) ?

Possible Answers:

$y=\frac{1}{3}x+5$

y=2x+19

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

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

y=3x-12

Correct answer:

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

Explanation:

The given line can be rewritten as $y=-\frac{1}{2}x+\frac{7}{10}$ , which has slope $m=-\frac{1}{2}$ .

If the new line is parallel to the old line, it must have the same slope. So we use the point-slope form of an equation to calculate the new intercept.

y=mx+b becomes $7=-\frac{1}{2}(-6)+b$ where b=4 .

So the equation of the parallel line is $y=-\frac{1}{2}x+4$ .

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Example Question #1 : How To Find The Equation Of A Parallel Line

Find the equation of a line parallel to y=12x-5 .

Possible Answers:

$y=\frac{1}{12}x-5$

y=.12x+2

$y=-\frac{1}{12}x-5$

y=12x+2

Correct answer:

y=12x+2

Explanation:

Since parallel lines share the same slope, the only answer that works is y=12x+2.

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Example Question #3 : How To Find The Equation Of A Parallel Line

Given the equation y=2x-13 and the point (-2,4) , find a line through the point that is parallel to the given line.

Possible Answers:

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

y=2x+8

y=2x-8

$y=\frac{1}{2}x+8$

y=2x+4

Correct answer:

y=2x+8

Explanation:

In order for two lines to be parallel, they must have the same slope. The slope of the given line is , so we know that the line going through the given point also has to have a slope of . Using the point-slope formula,

$y-y_{1}=m(x-x_1)$ ,

where represents the slope and y_1 and x_1 represent the given points, plug in the points given and simplify into standard form:

y-4=2(x-(-2))

y-4=2x+4

y=2x+8

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Example Question #64 : Algebra I

What line is parallel to y=2x+1 through (3,-9) ?

Possible Answers:

$y=\frac{1}{2}x-10$

y=-2x+3

y=2x-15

y=3x-9

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

Correct answer:

y=2x-15

Explanation:

Parallel lines have the same slopes. The slope for the given equation is . We can use the slope and the new point in the slope intercept equation to solve for the intercept:

y=mx+b

-9=2(3)+b

b=-15

Therefore the new equation becomes:

y=2x-15

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Example Question #4 : How To Find The Equation Of A Parallel Line

What line is parallel to $y=\frac{1}{2}x-2$ through (6,7) ?

Possible Answers:

3x-2y=4

3x+5y=8

2x+3y=5

-x+2y=8

x-2y=6

Correct answer:

-x+2y=8

Explanation:

Parallel lines have the same slope. The slope of the given line is $\frac{1}{2}$ .

Find the line with slope $\frac{1}{2}$ through the point (6,7) by plugging this informatuon into the slope intercept equation, y=mx+b :

$7=\frac{1}{2}(6)+b$ , which gives 7=3+b .

Solve for by subtracting from both sides to get b=4 .

Then the parallel line equation becomes $y=\frac{1}{2}x+4$ , and converting to standard form gives -x+2y=8 .

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Example Question #2 : How To Find The Equation Of A Parallel Line

Find the equation of a line parallel to the line that goes through points $\left ( 2,4 \right )$ and $\left ( 0,7 \right )$ .

Possible Answers:

y=3x+4

$y=\frac{2}{3}X+7$

$y=\frac{3}{2}X-5$

$y=-\frac{3}{2}X+7$

Correct answer:

$y=-\frac{3}{2}X+7$

Explanation:

Parallel lines share the same slope. Because the slope of the original line is $-\frac{3}{2}$ , the correct answer must have that slope, so the correct answer is

$y=-\frac{3}{2}X+7$

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Example Question #1 : Graphing

The vertices of a triangle are given by $(0,3), \; (0,5),\; and \; (-2,4)$ . The triangle is rotated about the origin by degrees clockwise. What are the new coordinates?

Possible Answers:

$(6,0), \; (10,0),\; and \; (8,4)$

$(4,1), \; (6,1),\; and \; (5,3)$

$(-9,0), \; (-15,0),\; and \; (-12,-6)$

$(-3,0), \; (-5,0),\; and \; (-4,-2)$

$(3,0), \; (5,0),\; and \; (4,2)$

Correct answer:

$(3,0), \; (5,0),\; and \; (4,2)$

Explanation:

The coordinates form a triangle in the second quadrant with a side along the y-axis. The rotation about the origin by degrees clockwise results in a triangle in the first quadrant with a side along the x-axis. There are two responses that give triangles along the x-axis:

$(3,0), \; (5,0),\; and \; (4,2)$ and

$(6,0), \; (10,0),\; and \; (8,4)$

A rotation and a dialation by a factor of is given by

$(6,0), \; (10,0),\; and \; (8,4)$ , so the correct answer is $(3,0), \; (5,0),\; and \; (4,2)$

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Example Question #61 : Algebra I

What is the y-intercept of the equation?

y=5x+5

Possible Answers:

(0,1)

(0,0)

(0,5)

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

(0,25)

Correct answer:

(0,5)

Explanation:

To find the y-intercept, we set the value equal to zero and solve for the value of .

y=5x+5

y=5(0)+5

y=0+5

y=5

Since the y-intercept is a point, we want to write our answer in point notation: (0,5) .

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Example Question #2 : How To Find X Or Y Intercept

What is the x-intercept of the equation?

$y=\frac{2}{3}x+ 12$

Possible Answers:

(-18,0

(6,0)

(-12,0)

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

(0,0)

Correct answer:

(-18,0

Explanation:

To find the x-intercept of an equation, set the value equal to zero and solve for .

$y=\frac{2}{3}x+ 12$

$0 =\frac{2}{3}x+12$

Subtract from both sides.

$0 -12 = \frac{2}{3}x +12 - 12$

$-12 = \frac{2}{3} x$

Multiply both sides by $\frac{3}{2}$ .

$(\frac{3}{2})(-12) = (\frac{2}{3} x)(\frac{3}{2})$

-18= x

Since the x-intercept is a point, we will want to write it in point notation: (-18,0

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Example Question #3 : How To Find X Or Y Intercept

What is the y-intercept of y=5x+20?

Possible Answers:

$\frac{1}{4}$

100

Correct answer:

Explanation:

To solve for the y-intercept, set the x value equal to zero:

y=5x+20

y=5(0)+20

y=20

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High School Math : Algebra I

Study concepts, example questions & explanations for High School Math

All High School Math Resources

Example Questions

Example Question #1 : How To Find The Equation Of A Parallel Line

Example Question #1 : How To Find The Equation Of A Parallel Line

Example Question #3 : How To Find The Equation Of A Parallel Line

Example Question #64 : Algebra I

Example Question #4 : How To Find The Equation Of A Parallel Line

Example Question #2 : How To Find The Equation Of A Parallel Line

Example Question #1 : Graphing

Example Question #61 : Algebra I

Example Question #2 : How To Find X Or Y Intercept

Example Question #3 : How To Find X Or Y Intercept

All High School Math Resources

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