Equations & Inequalities
3x + 2 < -2x - 3
x < -1
{(9,18), (0,36), (6,21), (6,22)}
Not a function; the x-value of 6 has two y-values
What is slope?
Change in y over change in x; rise over run; the steepness of a line
What is the slope-intercept equation?
y = mx + b
What is a system of equations?
Two equations that have the same two variables
8x - 2 = -9 + 7x
x = -7
{(-1,6), (4,2), (2,36)}
Function; every x-value has only one y-value
What equation do we use to find slope?
m = y2 - y1 / x2 - x1
What letter represents slope?
m
When we find solutions to a system of equations, what are we really finding?
All the points the lines have in common
-8 = -(x + 4)
x = 4
x y
-7 2
11 4
0 6
11 8
0 10
Not a function; the x-value of 11 has two y-values (or, the x-value of 0 has two y-values)
What is the slope between (1,0) and (4,8)?
m = 8/3
What letter represents the y-intercept?
b
What does one solution to a system of equations look like when graphed?
The lines cross each other
3x - 5 = -8(6 + 5x)
x = -1
x y
14 5
15 10
16 15
17 10
18 5
Function; every x-value has only one y-value
What is the slope between (2,1) and (-4,0)
m = 1/6
What is the slope-intercept equation of a line with a slope of -2 and a y-intercept of -7?
y = -2x - 7
What does no solution to a system of equations look like when graphed?
The lines are parallel
-5(-2x - 1) > -(-2x + 3)
x > -1
{(-1,4), (4,-1), (2, 4), (2,-1)}
Not a function; the x-value of 2 has two y-values
What is the slope between (-3,-1) and (-5,-2)?
m = 1/2
What is the slope-intercept equation of a line with a slope of 3/5 and a y-intercept of -9?
y = 3/5x - 9
What does infinite solutions to a system of equations look like when graphed?
The lines are the exact same line