1. Chapter 8 Review

2. Section 8.1 “Relations and Functions”
a pairing of numbers from one set, called the DOMAIN, with the numbers in another set, called the RANGE.
Set 1
Set 2
Domain
Range
Input
Output
X-coordinate
Y-coordinate

3. Each input must be paired with only ONE output
FUNCTION-
Is a relation in which for each input there is EXACTLY ONE output.
FUNCTION
NOT A FUNCTION
3 5
Each input must be paired with only ONE output

4. Solving Linear Equations
To find a SOLUTION, substitute the ordered pair into the equation and see if it produces a true statement.
2x – y = 5
Tell whether the ordered pair is a solution to the equation.
point
equation
substitution
check
(1, 3)
2x - y = 5
2(1) – 3 = 5
-1 = 5 NO
(2,-1)
2x - y = 5
2(2) – -1 = 5
5 = 5
YES

5. An equation is in function form when the equation is solved for y.
Linear Equation-
an equation whose graph is a line
4x + y = 9
Function form-
An equation is in function form when the equation is solved for y.
4x + y = 9
y = 9 – 4x
Solve the equation for y.

6. Section 8.3 “Using Intercepts”
x-intercept-
y-intercept-
the y-coordinate of the point where the graph crosses the y-axis
the x-coordinate of the point where the graph crosses the x-axis
To find the y-intercept, solve for ‘y’ when ‘x = 0.’
To find the x-intercept, solve for ‘x’ when ‘y = 0.’
Find the y-intercept of the graph 2x + 7y = 28.
Find the x-intercept of the graph 2x + 7y = 28.
2(0)+ 7y= 28
2x + 7(0)= 28
7y = 28
2x = 28
y = 4
x = 14

7. Section 8.4 “The Slope of a Line”
the ratio of the vertical change (the rise) to the horizontal change (the run) between any two points on a line.
Slope = rise = change in y
run change in x

8. Slope Review The slope m of a line passing through two points
and is the ratio of the rise change to the run. y
run
rise x

9. Section 8.5 “Graph Using Slope-Intercept Form”
a linear equation written in the form
y-coordinate
x-coordinate
y = mx + b
slope
y-intercept

10. Parallel Lines y = 3x + 2 y = 3x – 4
two lines in the same plane are parallel if they never intersect. Because slope gives the rate at which a line rises or falls, two lines with the SAME SLOPE are PARALLEL.
y = 3x + 2
y = 3x – 4

11. Perpendicular Lines y = -2x + 2 y = 1/2x – 4
two lines in the same plane are perpendicular if they intersect at right angles. Because slope gives the rate at which a line rises or falls, two lines with slopes that are NEGATIVE RECIPROCALS are PERPENDICULAR.
y = -2x + 2
½ and -2 are
negative reciprocals.
y = 1/2x – 4
4/3 and -3/4
are negative reciprocals.

12. Section 8.6 “Writing Linear Equations”
You can write a linear equation in slope-intercept form, if you know the slope (m) and the y-intercept (b) of the equation’s graph.
SLOPE-INTERCEPT FORM-
a linear equation written in the form
y-coordinate
slope
x-coordinate
y-intercept
y = mx + b

13. Calculate the slope of the line that
Write an equation of the line that passes through the given points. (-6, 0), (0, -24)
STEP 1
Calculate the slope of the line that
passes through (-6, 0) and (0, -24).
STEP 2
Write an equation of the line. The line crosses the y-axis at (0, -24). So, the y-intercept is -24.
y = mx + b
Write slope-intercept form.
y = -4x + (-24)
Substitute -4 for m and -24 for b.
The equation is y = -4x – 24.

14. Section 8.7 “Function Notation”
a linear function written in the form y = mx + b where y is written as a function f.
x-coordinate
f(x) = mx + b
This is read
as ‘f of x’
slope
y-intercept
f(x) is another name for y.
It means “the value of f at x.”
g(x) or h(x) can also be used to name functions

15. What is the value of the function f(x) = 3x – 15 when x = -3?
Linear Functions
What is the value of the function f(x) = 3x – 15 when x = -3?
A B C D. 8
f(-3) = 3(-3) – 15
Simplify
f(-3) = -9 – 15
f(-3) = -24

16. f(x) = 2x – 10 6 = 2x – 10 8 = x Linear Functions
For the function f(x) = 2x – 10, find the value of x so that f(x) = 6.
f(x) = 2x – 10
Substitute into the function
6 = 2x – 10
Solve for x.
8 = x
When x = 6, f(x) = 8