Chapter 2 Linear Relations & Functions

2-1 relations & functions Order pair – a pair of coordinates, written in the from ( x, y ), used to locate any point on a coordinate plane. Let plat a point (5,4). You go over 5,& up 4. Relation is a set of ordered pairs, such as the one right here. X =5 Y =4 Domain of a relation is the set of all first coordinates (x coordinates) from the ordered pair. Range is the set of all second coordinates (y coordinates) from the ordered pair. So… D = 5 R = 4 Cartesian coordinate plane is composed of the x-axis and the y-axis which meet at the origin (0,0) and divide the plane into for quadrants

Function is a special type of relation in which each element of the domain is paired with exactly one element of the range! Functions!!! Not Functions!!! If you want to know if a relation is a function, you can use the vertical test. Not a function cause the vertical line intersects the graph in two or more points. Is a function cause the vertical line intersects the graph in only one point.

Graph y = 3x +4 Y = 3x + 4 X Y 1(2) + 4 = 6 1(3) + 4 = 7 1(4) + 4 = 8

Function notation is an equation of y in terms if x can be rewritten so that y = f(x). For example: y = 1x + 7 can be written as f(x) = 1x + 7 What is f(x) = 1x + 7 if x = 2. f(2) = 1(2) + 7 f(2) = f(2) = 9

2-2 linear equations A linear equation could be x + y= 5. The Graph of a linear equation is always a straight line. As long as you go by the following conditions its easy to defined a easier equation, The Variables can have no exponents greater then 1. The Variables cannot be multiplied together. The Variables cannot be in the denominator The variables cannot be under a radical.

A Linear Function is a function whose ordered Paris satisfies a linear equation. A linear function is a function whose ordered pairs satisfies a linear equation. Any linear functions can be written y = mx + b, where m and b are real number. f(x)=10-5x : This is a linear function because it can be written as f(x)=-5x+10.m=5,b=10 These are not a liner equations, G(x)=x4 -5 :This is not a linear function because x has an exponent other then 1. H(x, y)=2xy : this is not a liner function because the two variables are multiplied together

Standard form of al linear Equation, Ax + By=C : A cannot be negative B & C cannot both be 0 y=2x y = 2 multiply each side by -1 so that A = or greater then 0. 2 – y = -2 A = 2 B = -1 C =-2

If You know where the line crosses the x and y axis, it would be much easier to graph the line. You can use the slandered form to find the intercepts. The x-intercept is the value of x when y = 0, and the y=intercept is the value of y when x = 0. 3x-4y-12= x-4y=12 3x-4(0)=12 3x-0=12 3x=12 3x/3=12/3 X=4 So Your x intercept is x = 4 So let find the x intercept. 3x - 4y - 12 = x - 4y = 12 3( 0) – 4y = 12 0 – 4y = 12 4y = 12 4y/4 = 12/4 y = 3 So your y intercept is y = 3

2-3 slope The slope of a line is the ratio of the change in y- coordinates to the corresponding change in x- coordinates. Slope = change in y-coordinates change in x-coordinates = y2 – y1 x2 – x1 The slope of a line is the same, no matter what two points on the line are used.

Now let fine the slope. (-1, 4) (1, -2) M= y2- y1 slope formula x2 – x1 = – (-1) =-6 2 or -3 simplify. So the slope of the line is - 3.

Graph the line passing through (-4, -3) with a slope of 2/3. o Graph the ordered pair (-4,-3). Then, according to the slope, go up 2 units and right 3 units. Plot the new point at (- 1, -1).

Write an equation in slop-intercept from for the line that has a slope of – 3/2 and passes through (-4,1). y = mx + b slope –intercept form. 1 = (-3/2) (-4) + b (x,y) = (-4,1), m= -3/2 1 = 6 + b simplify -5 = b subtract 6 from each side. The y-intercept is -5. So, the equation in slop- intercept form is y = -3/2x – 5.

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