Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

# 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
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

Solution ** 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. 