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**Lines, Lines, Lines!!! ~ Slope-Intercept Form**

The meaning of Variables in a line

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Introduction A Line is composed of an infinite number of points puts together. All points fit the pattern of a single formula. There are several ways we could write the formula: Standard Form Point-Slope Form Slope-intercept Form

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**Slope intercept form is:**

y = mx + b Our goal is to define each line where the “y” is alone on one side of the equation.

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**Notice that these equations are all solved for y.**

These equations are all in Slope-Intercept Form: Notice that these equations are all solved for y.

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

y = mx + b slope y-Intercept Now look at the equation below…… 2 What is the slope? ____________ 1 What is the intercept? ____________

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**Convert to Slope-Intercept Form**

Now Try this Convert to Slope-Intercept Form 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 - 3 What is the slope? ____________ -13 What is the intercept? ____________

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

y = mx + b slope y-Intercept 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

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

using their y-intercepts and slopes.

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**1. Plot the y-intercept as a point on the y-axis**

1. Plot the y-intercept as a point on the y-axis. The constant b = 1, so the y-intercept = 1. right 1 up 2 right 1 up 2 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.

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**1. Plot the y-intercept as a point on the y-axis**

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. down 1 down 1 right 1 right 1

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**1. Plot the y-intercept as a point on the y-axis**

1. Plot the y-intercept as a point on the y-axis. The constant b = -7, so the y-intercept = -7. right 3 up 5 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

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**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

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**The constant b = 8 is the y-intercept.**

The coefficient m = 3/2 is the slope.

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**The constant b = 1 is the y-intercept. **

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

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**The constant b = -3 is the y-intercept.**

The coefficient m = -6/5 is the slope.

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**The new modified equations are:**

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

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Student Activity You will now receive a worksheet. Turn the worksheet in when completed.

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**Do Not Disturb Work In Progress**

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Do Now Write the slope-intercept equation of this line.

Do Now Write the slope-intercept equation of this line.

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