Standard Form
What is Standard Form?
Ax + By = C
What is point-slope form?
y-y1 = m(x-x1)
2(x-10) = 5
2(x-10) = 5
2x - 20 = 5
2x = 25
x = 12.5
f(x) = 7x + 18
Moving a line up/down or left/right, but otherwise unchanged.
What is the x-intercept and y-intercept of the following equation?
5x + 2y = 20
x-intercept is (4, 0)
y-intercept is (0,10)
What is the point and the slope from this following equation?
y - 2 = 3(x + 4)
slope = 3
point = (-4, 2)
-6x > 9x + 8(-x + 0.5)
-6x > 9x + -8x + 4
-6x > x + 4
-7x > 4
x < -4/7
Sally buys a membership to an online clothing store that sends her a package of clothes each month. Each package she keeps is $70, and she paid a registration fee of $20. What is this function in slope-intercept form, where C = cost, and p = number of packages she keeps?
C(p) = 20 + 70p
What is the definition of reflection?
What is the slope of the following equation?
5x - 9y = 18
m=-A/B
m=-5/-9
m=5/9
Put the following equation into slope-intercept form:
y-8 = 2(x-4)
y - 8 = 2x - 8 (distributed)
y = 2x - 8 + 8 (added 8 to both sides)
y = 2x (combined like terms)
2(x - 3) = 1/4(x + 5)
2x = (1/4)x + 5/4 + 6
2x = (1/4)x + 29/4
7/4x = 29/4
7x = 29
x = 29/7
If f(x) = 5x2 + 2x + 1, what is f(5)?
f(5) = 5(5)2 + 2(5) + 1
f(5) = 125 + 10 + 1
f(5) = 136
Translate the following function up 5 units.
f(x) = 3x + 2
f(x) = 3x + 2 + 5
f(x) = 3x + 7
3x + 4y = 16
4y = 16 - 3x (subtract 3x from both sides)
y = 4 - (3/4)x (divide both sides by 4)
y = (-3/4)x + 4
Put the following equation into standard form:
y - 10 = 9(x - 3)
Put into slope intercept:
y = 9x - 18 + 10
y = 9x - 8
y - 9x = - 8 (subtract 9x to put Ax and By on the same side)
A small, private school has 8 more girls than boys. The ratio of girls to boys is 8 to 7. How many girls are there?
x + 8/x = 8/7
7(x+8) = 8x
7x + 56 = 8x
56 = x
There are 56 boys and 64 girls
f(2) = 2(2) + 7
f(2) = 11
g(3) = 3(3)2
g(3) = 3(9) = 27
f(2) + g(3) = 11 + 27 = 38
Reflect the following function across the x-axis. Then, translate it to the right by 9 units.
f(x) = 14x + 7
y = -14x - 7 (reflection)
y = -14(x-9) - 7 (right by 9)
Rearrange the following equation into Standard form:
y = 2/3x - 1/2
y - 2/3x = -1/2 (subtracted 2/3x from both sides)
3y - 2x = -3/2 (multiplied both sides by 3)
6y - 4x = -3 (multiplied both sides by 2)
4x - 6y = 3 (multiplied both sides by -1)
What is the equation of a function in point-slope that passes through the points (0,8) and (4,2)?
slope = (y2-y1)/(x2-x1) = (2 - 8)/(4-0) = -6/4 = -3/2
y - 8 = -3/2(x)
OR
y - 2 = -3/2(x-4)
There are two-thirds as many blue fish in a tank as there are red fish. There are seven more green fish as there are blue fish. There are half as many yellow fish as there are red fish. The number of fish total is 41. How many of each fish are there?
blue fish + red fish + green fish + yellow fish = 41
(2/3)x + x + (2/3)x + 7 + (x/2) = 41
(4/6)x + (6/6)x + (4/6)x + (3/6)x = 34
(17/6)x = 34
x = 12 red fish
8 blue fish (2/3 of 12)
15 green fish (8 + 7)
6 yellow fish (half of 12)
g(3) = 2(3)2
g(3) = 2(9)
g(3) = 18
f(18) = 3(18)
f(18) = 54
Shift the following function down 7, and to the right 3.
f(x) = x2 + 2x
f(x) = (x-3)2 + 2(x-3) - 7 (to the right 3)