Chapter 1
x + 4 =10
x =6
What do each of these symbols mean?
<
>
≤
≥
< : less than
> : greater than
≤ : less than or equal to
≥ : greater than or equal to
Is this a function?
(2, 4) (-2, 4) (0, 1) (4, 2) (4, -2)
No- the x values are not unique. There are two 4's.
2, -2, 0, 4, 4
What letter represents slope?
What letter represents the y-intercept?
m = slope
b = y-intercept
Is this a solution to the following systems:(2,1)
y = 3x - 5
x + y = 3
Yes
1 = 3(2) - 5
1 = 6 - 5
1 = 1
and
2 + 1 = 3
3 = 3
3x + 2 = 11
x = 3
2y + 8 < 24
Graph it:
y < 8
open circle ; pointed to the left
Is this linear?
(5, 1) (4, 0) (3, -1) (2, -2) (1, -3)
Yes ; the y and x values are going up by a consistent pattern.
Parallel slope to : -1/4
Perpendicular slope to : -1/4
parallel: -1/4
perpendicular: 4
How many solutions do you have when you have parallel lines?
No solution.
-10x - 11 = 29
x = -4
|x + 5| ≤ 10
solve and graph.
x ≥ 15 AND x ≤ 5
shade between (and makes land)
Which equation is considered linear?
y = 2 - 5x
y = -5x3
y = 2 - 5x2
y = -5/x
y = 2 - 5x
Graph the following:
y = -2x - 7
slope (m): -2
y-intercept (start on y-axis): -7
For which equation would you draw a solid line and shade below?
y < 3x + 1
y > 3x + 1
y ≥ 3x + 1
y ≤ 3x +1
y ≤ 3x +1
7x + 3 = 2x +13
x = 2
|2x - 4| ≥ 18
solve and graph.
x ≤ -7 OR x ≥ 11
shade out (like oars on a boat)
Evaluate the function:
y = 3x + 9 when x = 2
y=15
What is the equation of the line that passes through (-3, 1) and is parallel to
y = 4x + 1.
y = 4x +13
Solve by substitution:
2y - 4x = 2
y = -x + 4
(1, 3)
-3x - 32 = -2 ( 5 - 4x)
x = -2
|2x - 4| ≥ -18
Infinitely Many Solutions
Evaluate the function.
y = 2x + 8 when y = 4
x = -2
Write the equation of the line that passes through (-1, 4) and (2, -2).
y = -2x + 2
Solve by elimination:
2x - 5y = 11
6x + 4y = 14
*HINT: you will need to multiply 1 of the equations
(3, -1)