1. 3-3 Linear Equations A linear equation is an equation of a line.
A linear equation is an equation that can be written in STANDARD FORM
Where A, B, and C are any numbers
A & B are not both zero
A can not be a fraction or negative

2. Is it a linear equation? xy = 2 x2 = y2 3m – 2n = 8 3m – 2n = 0No
x2 = y2
3m – 2n = 8
Yes
3m – 2n = 0
4x2 – 3x = y
2m + 5m = 7n

3. Determine whether the equations are linear equations
Determine whether the equations are linear equations. If so, write the equation in standard form.
5x + 3y = z + 2
Not linear one too many variables
.75x = y + 8
Linear change to standard form Ax + By = C
.75x – y = 8 subtract y from both sides
3/4x – y = 8 change .75 to a fraction of 3/4
4(3/4x – y) = 4(8) multiply each side by denominator of 4
3x – 4y = 32 distribute
1/3y = -1
Linear
y = -3
y = x2 + 3
Not linear x is squared

4. X & Y Intercepts
X – intercept (aka zeros): The x-coordinate of the point at which the graph of an equation crosses the x-axis.
Where the y value is 0
Y – intercept: The y-coordinate of the point at which the graph of an equation crosses the y-axis.
Where the x value is 0
x-intercept
y-intercept

5. Let’s take a look at pg. 156 Check your Progress 2A & 2B
Determine the x-intercept, y-intercept, and zero.
None, 150, none
Remember – the x-intercept and the zero will always be the same!
Describe what the intercepts mean.
The y-intercept 150 means that the initial cost of the gym membership is $150.

6. Now take a look at pg. 157 Check your Progress #3
Use the table (in example #3) to determine the x-intercept, y-intercept, and zero of the graph of the function.
x = -2
y = -4
Zero: x = -2

7. Graphing by making a tablex
2x + 2 y
(x,y) -2
2(-2) + 2
(-2,-2) -1
2(-1) + 2
(-1,0)
2(0) + 2 2
(0,2) 1
2(1) + 2 4
(1,4)
2(2) + 2 6
(2,6)
Graph ½y – x = 1
Get y by itself
½y = x + 1
y = 2x + 2
Pick values for x and plug them in to get y.
Pick 2 negative, 0, and 2 positive numbers.

8. Now Graph it
(x,y)
(-2,-2)
(-1,0)
(0,2)
(1,4)
(2,6)

9. 3x + 4y = 12 Let x = 0 OR simply cover up 3x. What does y equal? 3
Plot it on the y-axis.
Let y = 0 OR simply cover up 4y.
What does x equal? 4
Plot it on the x-axis
Then use a straightedge and connect the dots.

10. X = 2 Y = 3 Y = 3 means y is 3 regardless of what x is.
Y = # is always a HORIZONTAL LINE!
X = 2 means x is 2 regardless of what y is.
X = # is always a VERTICAL LINE!

11. Try These – Pg. 158 #1-4, 7-8, 10 1. No 2. Yes; 3y = -2
3. Yes; 3x – 2y = 25
4. 25, -4; x – intercept: temp at 0. y – intercept: at time 0, temp is -4
7. y = 2x + 8
8. x = 3
10. x + 4y = 10

12. Homework #22
p (odd), 61-63, skip 37