The document provides information and examples about linear equations and functions. It discusses determining if equations are linear based on their standard form, graphing linear equations, identifying x- and y-intercepts, determining if a relation is a function, and solving equations that contain only an x-variable. Examples include graphing the equation y=-3x/4, finding the x-intercept of 2x-2=-4, and graphing the function 5x+2=7.

2. 1. A 72 ft. pipe is cut into two pieces of lengths in a 5:7
ratio. What are the lengths of the two pieces?
2. A shirt has been discounted 30% and is on sale for $36.00.
What was the original price of the shirt?
3. Find a number so that 20 more than one-third of the
number equals three-fourths of that number.
4. x + 2 + x - 1 = 2 5. x + 3 = x - 2
3 2 6 4
6. What is the
Unit Price?

3. Linear Equations form straight lines. How do we
determine if an equation is linear:
It can be rewritten in the form: Ax + By = C
This is the Standard Form of a linear equation where:
a.) A and B are not both zero.
b.) The largest exponent is not greater than 1
Determine Whether the Equations are Linear:
1. 4 - 2y = 6x 2. -4/5x = -2 3. -6y + x = 5y - 2
Remember:
This is to determine whether an equation is linear
(forms a straight line) or not. The standard form is also
used to determine x and y intercepts.

4. Graphing Equations: y = mx
Graph the equation and tell whether it is linear.
3x
y=–
4

5. Graphing Equations: y = mx
The equation y = – 3x
4
is a linear equation.

6. 1. (2,5) These numbers are called:
2. { (2,5); (3,7); (4,9) } This group of ordered pairs is a:
3. A certain type of relation is a function. Describe a function.
3. Equation with only one dependent var. for each independent
Determining a Function:
4a.) If you have a relation of{ (2,5); (3,7); (4,9) }, then
you can use _________ to determine function.
4b.) If the ordered
pairs are graphed, then
use this test:_________

7. 5. The x values of a relation are known as the _______
6. The y values form the __________
7. Input values of a function come from the ________
8. Once the function is calculated, the output forms
the ______
9. The dependent variable can also be written in:
_________ __________.
10. If the f(x) = 3/4x - 1/2, then solve for: f(3)

8. Test Review: Determining
Solutions to Equations
11. Is the point (-1,-2) a solution to the equation y = 2x - 4
12. Find three points that are a solution to: 2x = y + 4
Intercepts
13. Name the x and y intercepts
for lines A & B.
14. For each line, state whether it
is positive, negative, or neither.
15. Find the x and y intercepts
for: y = -3x + 6 and y - 2 = 4x

9. If you are solving an equation by using a
table, then you want the equation to be
in y = mx + c form. For example, if the
equation is 2x + y = 4, you want to rewrite
the equation as y = -2x + 4. You then plug
in values for x, and solve for y
or
You can put the equation in Standard Form, Ax + By = C
find the intercepts, and use the slope to find other points

10. As you know, every point on a coordinate plane is the
intersection of two variables, the independent x, and the
dependent y.
What if, however, your equation only has an independent x
variable? 2x - 2 = -4
These equations can still be solved by finding the x
intercept, since we know that at this point, y = 0

11. How is it Done?
Graph the equation: 2x - 2 = - 4
1. First, set the equation equal to zero: 2x + 2 = 0
2. Replace 0 with f(x)
3. Make a table
4. Graph the ordered pairs
Graph the function
Last Practice:
** Graph 5x + 2 = 7