2.3 and 2.4 Lines

2.3 LINEAR FUNCTIONS AND SLOPE-INTERCEPT FORM

2.4 MORE ABOUT LINEAR EQUATIONS

LINEAR FUNCTIONS

A linear function is a function whose graph is a line.

We represent a linear function with a linear equation.

INTERCEPTS

An intercept of a line is a point where a line crosses an axis. The y-intercept is the point at which the line

crosses the y-axis. The x-intercept is the point at which the line

crosses the x-axis.

TO FIND THE INTERCEPTS

1. Set x = 0 and solve for y2. Set y = 0 and solve for x3. List your solutions as ordered pairs

EXAMPLE: WHAT ARE THE INTERCEPTS OF THE EQUATION?

3 5 15x y

SLOPE – INTERCEPT FORM

The slope-intercept of an equation of a line is y = mx + b, where m is the slope of the line and (0, b) is the y-intercept.

EXAMPLE: WHAT IS AN EQUATION OF THE LINE

and the y-intercept is 1

5m 0, 3

EXAMPLE: WHAT IS AN EQUATION OF THE LINE

WORKING WITH LINEAR EQUATIONS

We can rewrite a linear equation in slope – intercept form by solving for y.

EXAMPLE: WRITE THE EQUATION IN SLOPE – INTERCEPT FORM. WHAT ARE THE SLOPE AND Y-INTERCEPT.

5 4 16x y

EXAMPLE: WRITE THE EQUATION IN SLOPE – INTERCEPT FORM. WHAT ARE THE SLOPE AND Y-INTERCEPT.

3 11

4 2x y

POINT – SLOPE FORM

Given a point and the slope of a line we can write the equation of the line in point – slope form

EXAMPLE: WRITING AN EQUATION GIVEN A POINT AND THE SLOPE

A line passes through with slope

What is an equation of the line?

5,23

5

EXAMPLE: WRITING AN EQUATION GIVEN A POINT AND THE SLOPE A line passes through with slope

What is an equation of the line?

7, 1 3

WRITING AN EQUATION GIVEN TWO POINTS

1. Find the slope

2. Substitute the slope and either point into the point-slope form

2 1

2 1

y ym

x x

1 1y y m x x

EXAMPLE

A line passes through (3, 2) and (5, 8). What is an equation of the line in point-slope form?

STANDARD FORM

Another form of the equation of a line is standard form.

The coefficients of x and y and the constant should be intgers

A should be postive!

WRITING AN EQUATION IN STANDARD FORM WITH INTEGER COEFFICIENTS

1. Isolate the constant2. Eliminate Fractions:

Multiply each side of the equation by the least common denominator of all fraction coefficients

EXAMPLE: WRITE THE EQUATION IN STANDARD FORM.

35

4y x