Lines, Lines, Lines!!!Lines, Lines, Lines!!!~~

Slope-Intercept FormSlope-Intercept Form

The meaning of Variables in a The meaning of Variables in a lineline

IntroductionIntroduction

A Line is composed of an infinite number A Line is composed of an infinite number of points puts together.of points puts together.All points fit the pattern of a single formula.All points fit the pattern of a single formula.There are several ways we could write the There are several ways we could write the formula:formula:

Standard FormStandard Form

Point-Slope FormPoint-Slope Form

Slope-intercept FormSlope-intercept Form

Slope intercept form is:

Our goal is to define each line where the “y” is alone on one

side of the equation.

These equations are all in Slope-Intercept Form:

Notice that these equations are all solved for y.

When an equation is in slope-intercept form:When an equation is in slope-intercept form:When an equation is in slope-intercept form:When an equation is in slope-intercept form:

What is the slope? ____________

2 1y x Now look at the equation below……

What is the intercept? ____________

2y + 26 = -6x

Step 1: Subtract both sides by 26

Step 2: Divide both sides by 2 to get y by itself

Step 3: Simplify all fractions

Now Try this Convert to Slope-Intercept Form

What is the slope? ____________

What is the intercept? ____________

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When an equation is in slope-intercept form:When an equation is in slope-intercept form:When an equation is in slope-intercept form:When an equation is in slope-intercept form:

b = y-intercept. This constant helps us identified where to begin our graph. We start our graph on this number of the y-axis. The y-intercept tells us that the line crosses the y-axis at this point.

m = slope. This constant is always the coefficient of the ‘x’ variable. It helps us find all of the remaining points of the line

On the next three slides we will graph the three equations:

using their y-intercepts and slopes.

1. Plot the y-intercept as a point on the y-axis. The constant b = 1, so the y-intercept = 1.

2. Plot more points by counting the slope up the numerator and to the right denominator. The coefficient m = 2, so the slope = 2/1.

up 2

right 1 up 2

right 1

1. Plot the y-intercept as a point on the y-axis. The constant b = -4, so the y-intercept = -4.

2. Plot more points by counting the slope up the numerator and right the denominator. The coefficient m = -1, so the slope = -1/1.right 1

down 1right 1

down 1

1. Plot the y-intercept as a point on the y-axis. The constant b = -7, so the y-intercept = -7.

2. Plot more points by counting the slope up the numerator and to the right denominator. The coefficient m = 5/3, so the slope = 5/3.

right 3

up 5

right 3

up 5

Graph the following equations:Graph the following equations:

They look different but they are not different.

Before we can graph them, it is always best to set them us in the Slope-intercept Form:

y = mx + b

The constant b = 8 is the y-intercept.The coefficient m = 3/2 is the slope.

The constant b = 1 is the y-intercept.The coefficient m = 9/7 is the slope.

Or

The constant b = -3 is the y-intercept.The coefficient m = -6/5 is the slope.

The new modified equations are:The new modified equations are:

Now you will have a much easier time graphing these equations… Now your turn to graph…

Student ActivityStudent Activity

You will now receive a You will now receive a worksheet. Turn the worksheet. Turn the worksheet in when worksheet in when

completed.completed.

Do Not DisturbDo Not DisturbWork In ProgressWork In Progress