Term
What are Linear Functions?
Linear functions are those whose graph is a straight line. Has the following form. y = f(x) = a + bx and it has one independent variable and one dependent variable.
8x-5<2x+10
x>5/6
2x+1=4
x=3/2
4x+4<9x+8
x>-4/5
What is the gradient formula?
y2-y1/x2-x1
What is the midpoint
The midpoint is halfway between the two end points: Its x value is halfway between the two x values. Its y value is halfway between the two y values.
(-1,2) (5,5)
m=2/3
6x+4<9x+12
x<8/-3
y-2=1/4 (x-7)
y=x/4+1/4
What is the midpoint formula?
M=(x1+x2/2 y1-y2/2)
What are Inequalities?
An inequality compares two values, showing if one is less than, greater than, or simply not equal to another value.
5x+3y=12
x-3y= -6
y= 2 1/3
(1,2) (4,5)
=3/3=1
10x + 9y = -29
y=-29-10x/9
What is the equation of a line formula
y-y1=m(x-x1)
What are Functions?
Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable). Functions are ubiquitous in mathematics and are essential for formulating physical relationships in the sciences.
8x + 4y = -60
8x - 8x + 4y = -60 - 8x
4y = -60 - 8x
4 4
y = -15 - 2x
y = -4x - 15
m=3x+4
m-4/3=x
8m+95<-87m+5
m>-90/95
Inverse formula
f(x) = variable + something example f(x)= 4x + 8
What are Graph inequalities?
There are three steps: Rearrange the equation so "y" is on the left and everything else on the right. Plot the "y=" line (make it a solid line for y≤ or y≥, and a dashed line for y< or y>) Shade above the line for a "greater than" (y> or y≥) or below the line for a "less than" (y< or y≤).
g(x)=2x+1/3x+4
x=1-4y/3y-2
5x + 2y = -39
y=-39-5x/2
4x-12<3x+39
x=51
What is the length of a line formula
d= (x2-x1) + (y2-y1)2