LINEAR EQUATIONS
SLOPE OF ANY HORIZONTAL LINE
Zero
40
3X - 7 > - 7
x > 0
What the graph of a system of equations looks like when there is no solution
What is the inverse of the function y = 5x - 1?
y = (x + 1)/5
(Switch x and y and solve for y!)
SLOPE-INTERCEPT FORM of a linear equation
y = mx + b
6.9 * 109 and 3.0 * 10-3
2.3 * 1012
-7x + 5 < - 9
x > 2
What types of systems have infinite solutions?
Systems where the slope and the y-intercept are the same for both equations.
Write a recursive formula for the following sequence: 1, 5, 25, 125...
a1 = 1
an = an - 1 * 5
This is a geometric sequence. If it was repeated addition it would be arithmetic!
Slope of any VERTICAL LINE
Undefined
(X + 5) / 6 > - 4
x > - 29
How many solutions a system of equations has when the graph shows INTERSECTING lines
one
It's just like finding slope! Use two points and find the change in y over the change in x.
The x value at the y-intercept is...
0
What line has a slope of 3 and goes through (2, 106)?
y = 3x + 100
28 < 4 - 4X
x < - 6
What methods can you use to solve a system of equations?
Graphing, substitution, elimination, elimination with multiplication
How do you know if you can combine terms?
If they have the same variable and the same exponent. (You can combine 3x2 and 5x2, but you can't combine it with 3x10!)
definition of SLOPE
What is "rise over run", or "rate of change" ?
Write the equation for a line that goes through the points (4, 40).
y = 7x + 12
| x - 2| > 3
x > 5 or x < -1
When lines intersect at 90 degree angles, what do we know about the slope?
The slopes of the lines are opposite (+ or - ) and reciprocal (the fraction flips)
Are you ready for the final?
Almost...keep studying! :)