Inequalities
5x + 10 > 14x - 8
x < 2
3a + 4b = 43 and -2a + 3b = 11
(5,7)
Definition of x - intercept and y - intercept
The x - intercept point where the line crosses the x - axis.
The y - intercept point where the line crosses the y - axis.
f(x) = -3x + 4
(y-4)/(-3)
Parallel.
y = 3x + 4 (4, 7)
y = 3x - 5
4x + 3 > 2x +11
x > 4
2x + y = 5 and 3x + y = 7
(2,1)
What is a positive slope looks like?
What about a negative slope?
Positive slope is left to right (up)
Negative slope is right to left (down)
f(x) = 3x - 1
(y + 1)/(3)
Perpendicular.
y = -1/3x + 2 (3, 6)
y = 3x - 3
13x - 12 < 3x + 13
x < 2 1/2
4𝑥 + 8𝑦 = −4 and 2𝑦 − 5𝑥 = 23
(-4,3/2)
Graph the points with the equation: y = 2x
y =2x
If x = 0 If x = 1 If x = -1
y = 2(0) y = 2(1) y = 2(-1)
y = 0 y = 2 y = -2
(0, 0) (1, 2) (-1, -2)
If f(x) = 1-2x and f(x) = 0
What is the value of x
0.5 or 1/2
Parallel.
y = 3x + 6 (4, 2)
y = 3x - 10
3x - 4 - 4 (2- x) ≥ 9
x ≥ 3
3𝑥 − 𝑦 = 23 and 2𝑥 + 3𝑦 = 8
(7,-2)
Graph the points with the equation: y = -2x - 4
y = -2x - 4
if x = -1 If x = 0 If x = 1.
y = -2(-1) - 4 y = -2(0) - 4 y = -2(1) - 4
y = 2 - 4 y = 0 - 4 y = -2 - 4
y = -2 y = -4 y = -6
(-1, -2) (0, -4) (1, -6)
f(x) = 7x -5
(y+5)/(7)
Perpendicular.
y = -4x + -2 (4, -4)
y = 1/4x - 5
-4(x - 6) > 3x - (5x - 6)
x < -9
Two simultaneous equations are given below, where 𝑝 and 𝑞 are constants.
( 3𝑥 − 𝑝𝑦 = 4 and 4𝑥 − 3𝑦 + 𝑞 = 0 )
The solution to these equations is 𝑥 = 1, 𝑦 = 2.
Find the value of 𝑝 and 𝑞.
q= 2
Provide a definition for the following terms.
1. Domain
2. Range
3. Gradient
4. Y-Intercept
5. X-Intercept
1. The set of X values - Input Values
2. The set of Y values - Output Values
3. The measurement used to show the steepness of a line
4. The point where the line crosses the Y-axis
5. The point where the line crosses the X-axis
g(x) = x/4 + 1
Solve For The Inverse
f-1(x) = 4(y-1)
Parallel and Perpendicular.
y = -5x + 1 (2, -1)
Parallel: y = -5x + 9
Perpendicular: y = 1/5x - 7/5
(1 2/5)