5.4 slope intercept form

Algebra Warm up:

pg. 243 # 44 to 52 even

5.4 The Slope - Intercept Form pg. 244 to 251

Recall --How do you find an equation from a table of values? (ch. 1)

1. Find the constant difference2. Find the intial value at 0.3. Substitute info into equation

The constant difference indicates a Linear Pattern!

Rate is constant!!!!!

The value when x = 0 is called the y - intercept.-the ordered pair where the line crosses the y axis

always (0, # on y axis)

Rate IS the slope!

In a linear equation (equation for a line):

y = mx + b

"y and x" REMAIN as the variables because they change depending on the number used for x

"m " represents the slope"b " represents the y-intercept

This equation is called the

Slope Intercept Form ( y = mx + b)

This equation can be used to:

Graph an equationFind points on a lineDescribe a situation with a constant

WHY is this important?

This helps to show what values occur at what point.

It helps to solve situations exactly when you need to know what will happen when you do something.

There are many different ways to use this information.

Method 1-- Finding an equation from a graph.

1. Start with a graph (find 2 points)2. Find the slope (rise and run)

Remember-counting the blocks up/down and left/rightDON'T forget-a graph going down and to the right is NEGATIVE

3. Find the y interceptLook at the graph (y intercept is the number where the line crosses the y axis

4. Substitute the info (m and b) into the slope intercept form of the equation ( y = mx + b)

Try it!

y = 2 x + 2

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Try again!!!

Follow the steps!!!

y = -3 x + -2 2

try each one!

Method 2: Graphing a line when given the equation 1. Find the y intercept from the equation

( it is the "b" or the number on the end AFTER the problem is in y intercept form)

2. Put that point on the y axis3. Find the slope from the equation ( it is the "m" or the

coefficient of the x )4. Starting at the y intercept point--APPLY the slope 5. Find at least three points including the y intercept6. Connect the dots to make a line7. Don't forget arrows on the ends

y = 6 x + 8 7

Let's try it. Graph y = 2 x + -2

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Again...

Graph y = -2 x + 3

And again-Practice makes perfect. y = -4 x + 2y = 2 x - 4

3

Now we can combine methods from Monday and today Method 3: Find an equation of a line when you are given 2 points.

NOW- you have no graph to look at soo.... 1. Find the slope but now you have to use that equation to find slope

y2 - y 1 x2 - x1

m =

2. Substitute the slope into the slope intercept form of the equation (m)3. Also substitute ONE of the original ordered pairs in for x and y4. Solve for "b"5. Go back to the orginal form of the equation (y = mx + b) when there

are NO numbers in it...AND substitute the "m" and the "b" and leave the "x" and "y" alone

Sounds like alot but it is easy!

Lets try one together. Write an equation in slope intercept form for the line containing the point ( 3, 3) and ( 5, 7)

(walk me through it)

Now you try....Write an equation in slope intercept form for the line containing the following points: a) (4, -2) (6, 9) b) ( -4, 7) (10, 0) c) (2,3) (3,2)

Lets talk about intercepts! The y intercept is easy to find

It is the "b" in the equation when it is in slope intercept form because x = 0. If you substitute 0 in for the x then you solve for y

y = 6 x - 9 y intercept = -9

The slope is also easy to find when it is in slope intercept form(it is ALWAYS the number in front of the "x" )

m = 6 The x intercept is a little harder. (where the line crosses the x axis)

Substitute 0 in for the y and solve for x.

(0) = 6 x -9 x = 9+9 +9 6 or 1 1/29 = 6x x intercept6 6

y = 6 (0) - 9y = -9

lets try it..Identify the x and y intercepts. Make sure to label them. a) y = -4x + 8 b) y = 3x - 15

Equations of Horizontal lines. RECALL-

-Horizontal lines have a slope of 0.-Because line does not slant-The y1 and y2 are the same number-slope is 0-THERFORE the "m" and the "x" cancel out becasue the " m " is 0-SOO... equation for this line

y = b where b is the y intercept ex. Find the equation of a line with points (2, 4) and (3, 4) find m m= 4-4 0

3-2 1 = = 0

Theny = 0 x + b(4) = 0 (2) + b4 = b

Theny = 0 x + 4y = 4

Equation for a horizontal line!

Equations for Vertical Lines RECALL:

-Slope is undefined-Graph is straight up and down-The x1 and x2 are the same number-They cancel each other out-SOO slope is undefined ( zero is on bottom)-THERFORE the equation y = mx + b is Nonexistant!

The equation then becomes

x = a where a is the x intercept

In a nutshell-- Horizontal line:

*equation is the y value on the y axis wherethe line crosses

y = (number crossing at on y axis)

Vertical Line

*equation is the x value on the x axis where the line crosses

x = (number crossing at on x axis)

Lets try...

Let's put it together: 1. Graph a line and write an equation in slope intercept form containing the points (2, 4) and ( -4, 3) 2. Graph a line and write an equation in slope intecept form containing the points (0,6) and (-2, -2)