Inter Algebra 3.1 Graphing Equations

Front 1

Cartesian Coordinate System

Back 1

1. Also called "Rectangular Coordinate System".

2. x-axis (or axis of the abscissa) is horizontal.

3. y-axis (or the axis of the ordinate ) is vertical.

4. Each point in the plane can be plotted (or graphed)

5. ordered pairs describes its position in terms of distances along each axis from the orgin.

6. Ordered pairs are represented represented by the notation (x,y).

Front 2

Solutions of Equations in Two Variables

Back 2

1. Consist of two numbers that form a true statement when subtituted into the equation.

2.A convienent notation for writing these numbers is as ordered pairs, (x,y).

3.If the equation contains other various ordered pair solutions, they should be written in alphabetical order.

Front 3

Linear Equation in Two Variables

Back 3

Is an equation that can be written in the form

Ax + By + C

where, A and B are not both 0.

This form is called Standard Form.

Note: all variable terms are on one side of the equal sign and the constants on the other.

Front 4

X - Intercept

Y -Intercept

Back 4

y-intercept = is the point where the graph crosses the y-axis

x-intercept = is the point where the graph crosses the x-axis

Front 5

Finding X & Y intercepts

Back 5

1. To find an x-intercept, let y = 0 and solve for x.

2. To find an y - intercept, let x = 0 and solve for y.

Front 6

Graph the Linear Equation

y = 1/3 x

Back 6

x | y
________
0 0
6 2
-3 -1

x = 0 x = 6 x = -3
y 1/3(0) y=1/3(6) y = 1/3(-8)
y=0 y=2 y=-1

Front 7

Graphing Non-Linear Equations

Back 7

1. Not all Equations in two variables are linear equations

2. Not all graphs of equations in two variables are lines.

Front 8

Graph

y = x2

Back 8

1. This equation is not linear, because the x2 term does not allow us to write it in the form Ax + By = C (standard form)

2. Its graph is not a line. It is a curve shaped like a U.

3. The curve has a spcial name caled Parabola.

x | y
_________
-3 9
-2 4
-1 1
0 0
1 1
2 4
3 9