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Business Finance

Answer the Mathematical Problems Involving the Slope

1.Metro Department Store's annual sales (in millions of dollars) during 5 years were
Annual Sales, y
Year, x
5.8
1
6.1
2
7.2
3
8.3 9
4 5
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)
y = 0.9x + 1
B)
y = 0.8x + 5
C)
y = 0.6x + 4
2.Find the slope of the line shown in the figure.
A)
B)m = -1
C)m = 1
D)
E) not defined
3.Find the slope of the line that passes through the given pair of points. (-1, 2) and (3, 4)
A)
B)
C)
D)
4.Find the slope of the line that passes through the given pair of points. (2, 2) and (8, 5)
A) -1/2
B) -2
C) 10/7
D) 7/8
E) 1/2
Find the slope of the line that passes through the pair of points.
and
A)
B)
C)
D)
E)
6.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.
7.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
8.If the line passing through the points
the points
and
and
is parallel to the line passing through
, what is the value of a?
A) a = 32
B) a = 35
C) a = 31
D) a = 34
E) a = 33
9.Find an equation of the line that passes through the point (7, 6) and has the slope m =
A)
B)
C)
D)
E)
10.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
11.Find an equation of the line that passes through the points.
and
A)
B)
C)
D)
E)
12.Find an equation of the line that has slope
A)
and y-intercept
.
B)
C)
D)
13. Write the equation
in the slope-intercept form and then find the slope and y-
intercept of the corresponding line.
A)
B)
C)
D)
14.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
15.Sketch the straight line defined by the linear equation by finding the x- and y- intercepts.
A)
B)
C)
D)
16.Sketch the straight line defined by the linear equation by finding the x- and y- intercepts.
A)
B)
C)
D)
E)
17.Metro Department Store's annual sales (in millions of dollars) during 5 years were
Annual Sales, y
Year, x
5.8
1
6.3
2
7.1
3
8.3
4
9
5
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)
18.Determine whether the statement is true or false. If it is true, explain why it is true. If it is
false, give an example to show why it is false. The lines with equation
, where
and
and
, are perpendicular to each other.
A) True. The slopes of the lines are
and
respectively;
B) False. The slopes of the lines are
and
respectively;
,
, so
,
, so
.
.
19. 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) y = 8/5x + 9/5
B) y = 8/5x - 9/5
C) y = - 8/5x – 9/5
D) y = - 8/5x + 9/5
E) y is not a linear function of x.
20.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.
21. Determine whether the equation defines y as a linear function of x. If so, write it in the form
y = mx + b.
A)
B)
C)
D) y is not a linear function of x.
22. Determine whether the equation defines y as a linear function of x. If so, write it in the form
y = mx + b.
A)
B)
C)
D)
E) y is not a linear function of x.
23.Determine whether the equation defines y as a linear function of x. If so, write it in the form y
= mx + b.
A)
B)
C)
D) y is not a linear function of x
24. Find the constants m and b in the linear function
A)
B)
C)
D)
so that
and
E)
25.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)
...

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