Algebra Period 3 (Wednesday)

Linear Equations and Their Graphs 7-3

Equations whose graphs are lines are linear equations.
Must have only 1st powers only, no products or variables and no variables in the denominator.
Examples of linear equations:

y = 2x + 1 y - 3x = -2 5y = -4 9x - 15y = 7

Examples of Nonlinear Equations

y = x² - 4 x² + y² = 16 y = 2/x xy = 3

Since two points determine a line, plotting 2 points is sufficient for graphing linear equations. We should, HOWEVER, use a third point as a check!!

Graph the equation 2y - 4 = 4x

solve for y first

y = 2x + 2
find three solutions by setting up a T-chart and choosing values for x

if x = 0 y = 2(0) + 2 y = 2

if x = 1 y = 2(1) + 2 y = 4

if x = -2 y = 2(-2) = 2 y = -2

Plot the points ( 0,2) ( 1, 4) and ( -2, -2) AND DRAW the line containing those points.

Every point on the line is a solution to the linear equation!!

We can graph a linear equation by finding any two points that belong to the graph. Often the easiest points are where the graph crosses the axes.

The x- intercept of a line is the x-coordinate of the point where the line intercepts the x-axis.

The y- intercept of a line is the y-coordinate of the point where the line intercept the y-axis.

Graph 4x + 3y = 12 using intercepts

To find the x-intercept, let y = 0
then 4x + 3(0) = 12
4x = 12
x = 3 the x intercept is 3. WE plot the point (3,0)

To find the y-intercept, let x = 0
then 4(0) + 3y = 12
y = 4 the y intercept is 4 We plot the point (0,4)

Connect the two points and draw the line containing them. Make sure to always include arrows on your lines.

The standard form of a linear equation in two variables is
Ax + By = C, where A, B, and C are constants and
A and B are not BOTH zero.

5x + 7y = 35 3x -2y = 6 are examples of equations in standard form

y = 3 will be a line parallel to the x-axis written in standard form
0X + 1Y = 3 you can see that for any value of x y = 3. Thus, any ordered pair (x,3) such as (0,3), or (4,3) or even (-20, 3) would be a solution.
The line is parallel to the x-axis with y=intercept 3.


x = -5 will be a line parallel to the y-axis.