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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

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4 Diagnostic Tests 263 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #7 : Points And Lines

Which of the following lines contains the point (1,9) ?

Possible Answers:

4x+12y=-53

17x-3y=3

y=x+9

x-9y=77

3y - 15 =12x

Correct answer:

3y - 15 =12x

Explanation:

To solve for a question like this, the easiest thing to do is to plug in your and values to see what happens. If you get two numbers equal to each other when they are, in fact, unequal, you do not have a working case.

For example, consider the wrong option, y=x+9

Substitute in your values, and you get:

9=1+9 or 9=10

Now, for your correct option, you get:

3y - 15 =12x

3 * 9 - 15 =12*1

27-15=12

12=12

This certainly makes sense! It also means that the point is on the line in question!

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Example Question #5 : Points And Lines

Which of the following points is on the line y=-x+7 ?

Possible Answers:

(5,-2)

(-7,0)

(4,3)

(3,10)

(8,1)

Correct answer:

(4,3)

Explanation:

Upon substitution of the answer choices, we will need to satisfy the equation, by plugging in the x and y-values of the points given.

$(8,1): 1\neq-8+7$

$(5,-2): -2\neq -5+7$

$(3,10): 10 \neq -3+7$

$(-7,0): 0\neq -(-7)+7$

The answer is: (4,3)

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Example Question #5 : Points And Lines

Find the equation of the line given the two points (0,2) and (-2,3) .

Possible Answers:

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

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

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

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

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

Correct answer:

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

Explanation:

The equation of a line in slope-intercept form is y=mx+b .

Write the formula for slope.

$m=\frac{y_2-y_1}{x_2-x_1}$

Substitute the points.

$\frac{3-2}{-2-0} = -\frac{1}{2}$

The y-intercept from the point (0,2) means that b=2 .

The equation of the line is: $y=-\frac{1}{2}x+2$

The answer is: $y=-\frac{1}{2}x+2$

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Example Question #11 : Points And Lines

Given the points (9,-1) and (3,9) , what is the equation of the line?

Possible Answers:

3x-2y =14

$y= \frac{3}{2}x+14$

$y+1 = -\frac{5}{3}(x-9)$

$y+1 = -\frac{10}{3}(x-9)$

3x-2y =-14

Correct answer:

$y+1 = -\frac{5}{3}(x-9)$

Explanation:

The equation of the line is defined in the following forms:

Point-slope form: y-y_1 = m(x-x_1)

Standard form: Ax+By=C

Slope intercept form: y=mx+b

Find the slope of the two points using the slope formula.

$m = \frac{y_2-y_1}{x_2-x_1} = \frac{9-(-1)}{3-9} = \frac{10}{-6} = -\frac{5}{3}$

Using the slope and any point (9,-1) or (3,9) , we can substitute either into the point-slope form.

$y-(-1) = -\frac{5}{3}(x-9)$

The answer is: $y+1 = -\frac{5}{3}(x-9)$

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Example Question #11 : Points And Lines

Find the slope given the two points: (2,-3) and (6,-9)

Possible Answers:

$-\frac{3}{2}$

$-\frac{1}{5}$

$-\frac{2}{5}$

Correct answer:

$-\frac{3}{2}$

Explanation:

Write the slope formula.

$m = \frac{y_2-y_1}{x_2-x_1}$

Substitute the points.

$m = \frac{-9-(-3)}{6-2} = \frac{-6}{4} = -\frac{3}{2}$

The answer is: $-\frac{3}{2}$

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Example Question #311 : Algebra

Which of the following points is on the line 4x-8y=12 ?

Possible Answers:

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

(4, 2)

(3, 0)

$(2, \frac{3}{4})$

Correct answer:

(3, 0)

Explanation:

In order for a point to be on the line, the point must satisfy the equation given. Thus, plug in the and coordinates to see if they will give you a true equation.

If you plug in (3, 0) into the equation, you will get the following:

4(3)-8(0)=12

12=12

Thus, (3, 0) satisfies the equation and must be on the line.

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Example Question #141 : Linear Algebra

Which of the following points is on the following line?

y=-12x+6

Possible Answers:

(-2,-18)

(4,4)

(0,6)

(0,-4)

Correct answer:

(0,6)

Explanation:

Which of the following points is on the following line?

y=-12x+6

(0,6) (4,4) (0,-4) (-2,-18)

So, to test this, we can plug in each choice and solve to see if they make sense.

To save time, let's test the easier ones first. Recall that anything times 0 is 0, so we should try out the options with 0's first.

Recall that ordered pairs represent an x and a y value with the x coming first: (x,y)

y=-12x+6

(0,-4)

-4=-12(0)+6

-4=0+6

$-4\neq6$

So, this is not our answer. However, it does give us a hint as to the correct answer.

When we plugged in 0 for x, we got 6 on the right hand side. This means that if we plug in 0 for x, then we should get 6 for y. So, let's try out our next point.

y=-12x+6

(0,6)

6=-12(0)+6

6=6

So, our answer must be (0,6)

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Example Question #11 : Points And Lines

Which of the following points lies on the line 7x-8y=10 ?

Possible Answers:

$(-4, -\frac{7}{2})$

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

$(5, \frac{13}{8})$

(-2, -3)

Correct answer:

(-2, -3)

Explanation:

In order for a point to be on a line, the point must satisfy the equation. Plug in the values of and from the answer choices to see which one satisfies the equation.

Plugging in (-2, -3) will give the following:

7(-2)-8(-3)=10

-14+24=10

10=10

Since (-2, -3) satisfies the given equation, it must be on the line.

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Example Question #14 : Points And Lines

Find the y-coordinate which would would make the slope between the following points equal to 5.

(13,65) (43,y_2)

Possible Answers:

y_2=175

y_2=215

y_2=-225

y_2=115

Correct answer:

y_2=215

Explanation:

Find the y-coordinate which would would make the slope between the following points equal to 5.

(13,65) (43,y_2)

To find the slope of a line, use the following formula:

$m=\frac{y_2-y_1}{x_2-x_1}$

Now, we know all of these values except one. Let's find it.

$5=\frac{y_2-65}{43-13}\rightarrow5=\frac{y_2-65}{30}$

$5=\frac{y_2-65}{30} \rightarrow 150=y_2-65$

$150=y_2-65\rightarrow 150+65=y_2$

y_2=215

So, our answer is

y_2=215

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Example Question #861 : Ged Math

Solve the equation by factoring:
$\small 2x^2-2x-4=0$

Possible Answers:

$\small x=1\ or\ x=2$

$\small x=-1\ or\ x=2$

$\small x=1\ or\ x=-2$

$\small x=-1\ or\ x=-2$

Correct answer:

$\small x=-1\ or\ x=2$

Explanation:

$\small 2x^2-2x-4=2(x^2-x-2)=2(x+1)(x-2)=0$

Therefore:

$\small x+1=0\ or\ x-2=0$

$\small x+1-1=0-1\ or\ x-2+2=0+2$

$\small x=-1\ or\ x=2$

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GED Math : GED Math

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #7 : Points And Lines

Example Question #5 : Points And Lines

Example Question #5 : Points And Lines

Example Question #11 : Points And Lines

Example Question #11 : Points And Lines

Example Question #311 : Algebra

Example Question #141 : Linear Algebra

Example Question #11 : Points And Lines

Example Question #14 : Points And Lines

Example Question #861 : Ged Math

All GED Math Resources

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