Slope
Find the slope of the line that passes through the points (-1 , 0) and (3 , 8).
The slope m is given by
m = (y2 - y1) / (x2 - x1) = (8 - 0) / (3 - (-1)) = 2
Find the maximum or minimum value of f(x) = 2x2 + 3x - 5
f has a minimum value equal to -49/8
Solve for b:
-7 = b - 3
b = -4
WORK
-7 = b - 3
-7 +3 = b - 3 +3
-4 = b
Solve for x:
2x + 3 = 15
x = 6
WORK
2x + 3 = 15
2x + 3 - 3 = 15 - 3
2x = 12
(2x)/2 = 12/2
x = 6
Solve for m:
5 = 5m - 23 + 2m
m =4
WORK
5 = 5m - 23 + 2m
5 = 5m + 2m - 23
5 = 7m - 23
5 + 23 = 7m - 23 + 23
28 = 7m
28/7 = 7m/7
4 = m
Find the slope of the line that passes through the points (2 , 0) and (2 , 4).
The slope m is given by
m = (y2 - y1) / (x2 - x1) = (4 - 0) / (2 - 2) = 4 / 0
Division by zero is not allowed in maths. Therefore the slope of the line defined by the points (2 , 0) and (2 , 4) is undefined. The line through the points (2 , 0) and (2 , 4) is perpendicular to the x axis.
Find the range of f(x) = -x2 + 4x - 5
range: (- infinity , -1]
Solve for x:
x/3 = 2
x = 6
WORK
x/3 = 2
x/3 *3 = 2 *3
x = 6
Solve for a:
(1/2)a + 5 = 18
a = 26
WORK
(1/2)a + 5 = 18
(1/2)a + 5 - 5 = 18 - 5
(1/2)a = 13
2*(1/2)a = 13*2
a = 26
Solve for x:
(x + 4) + 2x = 67
(x + 4) + 2x = 67
x + 2x + 4 = 67
3x + 4 = 67
3x + 4 - 4= 67 - 4
3x = 63
3x/3 = 63/3
x = 21
Find the slope of the line that passes through the points (7 , 4) and (-9 , 4).
The slope m is given by
m = (y2 - y1) / (x2 - x1) = (4 - 4) / (- 9 - 7) = 0 / -16 = 0
The line defined by the points (7 , 4) and (-9 , 4) is parallel to the x axis and its slope is equal to zero.
Find the vertex of the graph of f(x) = 3x2 + 6x - 10
vertex at: (-1 , -13)
Solve for x:
5x = 20
x = 4
WORK
5x = 20
5x/5 = 20/5
x = 4
Solve for t:
-t + 8 = 3
t = 5
WORK
-t + 8 = 3
-t + 8 - 8= 3 - 8
-t = -5 [which is the same thing as -1t = -5]
-1t/-1=-5/-1
t = 5
Solve for x:
-8(2x - 1) = 36
x = -7/4
WORK
-8(2x - 1) = 36
-16x + 8 = 36
-16x + 8 - 8 = 36 - 8
-16x = 28
-16x/(-16) = 28/(-16)
x = -7/4
What is the slope of the line -7y + 8x = 9
We first find the slope of the line defined by points A and B
m(AB) = (y2 - y1) / (x2 - x1) = (1 - (-1)) / (2 - 0) = 1
We next find the slope of the line defined by points A and C
m(AC) = (3 - (-1)) / (- 4 - 0) = 4 / - 4 = -1
The product of the slopes m(AB) and m(AC) is equal to -1 and this means that the lines defined by A,B and A,C are perpendicular and therefore the triangle whose vertices are the points A, B and C is a right triangle.
Find the maximum or minimum value of f(x) = -3x2 + 9x
f(x) has a maximum value equal to 27/4
Solve for m:
(4/5)*m = 28
m = 35
WORK
(4/5)*m = 28
(5/4)*(4/5)*m = 28*(5/4)
m = 35
Solve for x:
(x – 7)/3 = -12
x = -29
WORK
(x – 7)/3 = -12
3*((x – 7)/3)= -12*3
x – 7 = -36
x – 7 + 7= -36 + 7
x = -29
Solve for x:
3.5 - 0.02x = 1.24
x = 113
WORK
3.5 - 0.02x = 1.24
100*(3.5 - 0.02x) = 1.24*100
350 - 2x = 124
350 - 350 - 2x = 124 - 350
-2x/(-2) = -226/(-2)
x = 113
What is the slope of the line y = 9?
The given equation
-7y + 8x = 9
Rewrite the equation in slope intercept form.
- 7y = - 8x + 9
y = (8/7) x - 9/7
The slope of the given line is 8/7
Find the range of f(x) = x2 + 5x - 2
range given by interval: [-33/4 , + infinity)
Solve for p:
-2.54 = p + 7.17
p = -9.71
WORK
-2.54 = p + 7.17
-2.54- 7.17 = p + 7.17- 7.17
p = -9.71
Solve for x:
-24 = -10x + 3
x = 2.7
WORK
-24 = -10x + 3
-24 - 3= -10x + 3 - 3
-27 = -10x
-27/(-10)=-10x/(-10)
2.7 = x
Solve for x:
3x/4 - x/3 = 10
x = 24
WORK
3x/4 - x/3 = 10
9x/12 - 4x/12 = 10
5x/12 = 10
12*(5x/12) = 10*12
5x/5 = 120/5
x = 24