# Math Straight Lines and Linear Functions

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If you think the statement is true, then prove it. On the other hand, if you think the statement is false, then give an example that disproves the statement. For example, the statement “If and are real numbers, then a – b = b – a” is false and an example that disproves it may be constructed by taking a = 3 and b = 5. For these values of a and b, we find a – b = 3 – 5 = -2 but – a = 5 – 3 = 2 and this shows that – b ≠ b – a. Such an example is called a ≠counterexample.

1. True or false. The slope of a horizontal line is undefined.
2. True or false. Suppose the slope of a straight line L is -3/4 and P is a given point on L. If Q is a point on L lying 2 units to the right of P, then Q is situated 3/2 units below P.
3. True or false. The y-intercept of the straight line with equation Ax By = 0 is –C/(B ≠ 0).
4. True or false. If a line L1 has equation mx b, where and are constants with m ≠ 0,then an equation of a line L2 perpendicular to L1 has the form  , where C is a constant.
5. True or false. Suppose an asset is being depreciated linearly. Then the rate of depreciation of the asset is given by the negative of the slope of the depreciation line.
6. True or false. If R and C are linear revenue and cost functions, respectively, and (x0p0) is the breakeven point, then P(x) > P(x0) if x > x0, where P is the profit function.
7. True or false. The least-squares line must pass through at least one of the data points.
1. Metro Department Store’s annual sales (in millions of dollars) during 5 years were
 Annual Sales, y 5.8 6.1 7.2 8.3 9 Year, x 1 2 3 4 5
1. Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L.
 A. B. C.

4 points

Question 2

1. Find the slope of the line shown in the figure.
 A. B. C. D. E.

4 points

Question 3

1. Find the slope of the line that passes through the given pair of points.

(-1, 2) and (3, 4)

 A. B. C. D.

4 points

Question 4

1. Find the slope of the line that passes through the given pair of points.

(2, 2) and (8, 5)

 A. B. C. D. E.

4 points

Question 5

 A. B. C. D. E.

4 points

Question 6

1. Determine whether the lines through the given pairs of points are parallel. A (2, – 3), B (- 2, – 11) and C (1, 2), D (- 1, 6)
 A. The lines through the given pairs of points are not parallel. B. The lines through the given pairs of points are parallel.

4 points

Question 7

1. If the line passing through the points (2, a) and (5, – 3) is parallel to the line passing through the points (4, 8) and (- 5, a + 1) , what is the value of a?
 A. a = -8 B. a = 4 C. a = -4 D. a = 8

4 points

Question 8

 A. B. C. D. E.

4 points

Question 9

 A. B. C. D. E.

4 points

Question 10

1. Find an equation of the line that passes through the points (1, 4) and ( -7, -4)
 A. y = 7x + 7 B. y = x + 3 C. y = 3x – 7 D. y = 3x – 3

4 points

Question 11

 A. B. C. D.

4 points

Question 12

 A. B. C. D.

4 points

Question 13

 A. B. C. D.

4 points

Question 14

1. Find an equation of the line passing through the origin and parallel to the line passing through the points (2,8) and (4,12).
 A. y = 2x + 4 B. y = 2x C. y = 3x D. y = 4x – 2

4 points

Question 15

 A. B. C. D.

4 points

Question 16

 A. B. C. D. E.

4 points

Question 17

1. Metro Department Store’s annual sales (in millions of dollars) during 5 years were
 Annual Sales, y 5.8 6.3 7.1 8.3 9 Year, x 1 2 3 4 5
1. Plot the annual sales (y) versus the year (x) and draw a straight line L through the points corresponding to the first and fifth years and derive an equation of the line L.
 A. B. C.

4 points

Question 18

 A. B.

4 points

Question 19

1. Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b. 8x = 5y + 9
 A. B. C. D. E. y is not a linear function of x.

4 points

Question 20

1. Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b. x = 3y – 9
 A. B. C. D. y is not a linear function of x.

4 points

Question 21

 A. B. C. D. y is not a linear function of x.

4 points

Question 22

 A. B. C. D. E. y is not a linear function of x.

4 points

Question 23

 A. B. C. D. y is not a linear function of x

4 points

Question 24

 A. B. C. D. E.

4 points

Question 25

1. Find the constants m and b in the linear function f(x) = mx + b so that f(1) = 2 and the straight line represented by f has slope – 1.
 A. B. C. D.

4 points