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GED Math : Linear Algebra

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Example Questions

Example Question #11 : Points And Lines

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

Possible Answers:

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

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

3x-2y =-14

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

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 #11 : Points And Lines

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 #11 : Points And Lines

Which of the following points is on the following line?

y=-12x+6

Possible Answers:

(0,6)

(0,-4)

(-2,-18)

(4,4)

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 #12 : Points And Lines

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

Possible Answers:

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

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

(-2, -3)

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

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 #141 : Linear Algebra

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=115

y_2=175

y_2=-225

y_2=215

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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All GED Math Resources

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GED Math : Linear Algebra

Study concepts, example questions & explanations for GED Math

All GED Math Resources

Example Questions

Example Question #11 : Points And Lines

Example Question #11 : Points And Lines

Example Question #11 : Points And Lines

Example Question #11 : Points And Lines

Example Question #12 : Points And Lines

Example Question #141 : Linear Algebra

All GED Math Resources

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