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Linear Equations and Inequalitie
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Graphing Equivalent Fractions Lesson Plan
Investigating Liner Equations Using Graphing Calculator
Graphically solving a System of two Linear Equatio
Shifting Reflecting Sketching Graph
Graphs of Rational Functions
Systems of Equations and Inequalities
Graphing Systems of Linear Equat
LINEAR FUNCTIONS: SLOPE, GRAPHS AND MODELS
Solving Inequalities with Absolute Values
Solving Inequalities
Solving Equations & Inequalities
Graph the rational function
Inequalities and Applications
Inequalities
Using MATLAB to Solve Linear Inequalities
Equations and Inequalities
Graph Linear Inequalities in Two Variables
Solving Equations & Inequalities
Teaching Inequalities:A Hypothetical Classroom Case
Graphing Linear Inequalities and Systems of Inequalities
Inequalities and Applications
Solving Inequalities
Quadratic Inequalities
Inequalities
Solving Systems of Linear Equations by Graphing
Systems of Equations and Inequalities
Graphing Linear Inequalities
Inequalities
Solving Inequalities
Solving Inequalities
Solving Equations Algebraically and Graphically
Graphing Linear Equations
Solving Linear Equations and Inequalities Practice Problems
Graphing Linear Inequalities
Equations and Inequalities
Solving Inequalities

LINEAR FUNCTIONS: SLOPE, GRAPHS AND MODELS

•Find the y-intercept of a line from the
equation y = mx + b or f(x) = mx + b.

•Given two points on a line, find the
slope; given a linear equation, derive
the equivalent slope-intercept equation
and determine the slope and the y-intercept.

•Solve applied problems involving slope.

Linear Function

A linear function f is any function that can be
described by f(x) = mx + b.

Objective

Find the y-intercept of a line from the
equation y = mx + b or f(x) = mx + b.

Example A

Graph f (x) = 3x and g(x) = 3x + 2
using the same set of axes.

Solution

Notice that the graph of
y = 3x + 2 is the graph of
y = 3x shifted, or translated,
2 units up.

y-Intercept of f(x) = mx + b

The y-intercept of the graph of
f(x) = mx + b is the point (0, b)
or, simply, b.

Example B

For each equation, find the y-intercept.

Solution

a) y = −3.1x + 7 (0, 7) is the y-intercept.

(0, –9) is the y-intercept.

Objective

Given two points on a line, find the
slope; given a linear equation, derive
the equivalent slope-intercept equation
and determine the slope and the
y-intercept.

Slope

The slope of the line containing points
(x₁, y₁) and (x₂, y₂) is given by

Example C

Graph the line containing the points (3, –2)
and (7, 5) and find the slope.

Solution

Example D

Determine the slope and y-intercept of the
line given by

Solution

The equation is written in the form y = mx + b,
simply read the slope and y-intercept from the

Example E

Determine the slope and y-intercept of the
line given by 4x − 7 y = 2.

Solution
First solve for y so we can easily read the
slope and y-intercept.

The slope is 4/7 and the y-intercept is (0, –2/7).

Objective

Solve applied problems involving
slope.

Some applications use slope to measure the steepness.
For example, numbers like 2%, 3%, and 6% are often
used to represent the grade of a road, a measure of a
road’s steepness. That is, a 3% grade means that for
every horizontal distance of 100 ft, the road rises or
drops 3 ft.
Slope can also be considered as a rate of change.

Example F
Find the slope (or grade) of the treadmill.

Solution

The grade of the treadmill is 7.6%.
** Reminder: Grade is slope expressed as a percent.

Example G Wanda’s Hair Salon has a graph
displaying data from a recent day of work.

a) What rate can be
determined from the
graph?
b) What is that rate?

Solution
a) We can find the rate
Number of haircuts per
hour.