Slope for Algebra 2

Category: Education

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By: Umesh (121 month(s) ago)

Oops, by first slide i meant of "Exponentials" lesson by Dev and Deb!

By: Umesh (121 month(s) ago)

Nice work creating these, very useful! And funny (first slide!)

Presentation Transcript

Slope : 

Slope Phil and Ethan

-How to find slope- : 

-How to find slope- Defined as “Rise over Run” Two simple equations to find slope

-Equations- : 

-Equations- ∆y ∆x y2-y1 x2-x1

-Examples- : 

-Examples- Data Points: (3, 3) (8, 6) 1) ∆y = (6-3) ∆x = (8-3) 3 5

-Practice- : 

-Practice- Data Points: (-3, 4) (6, -5) Find the Slope Answer: -1

-Slope Intercept Form- : 

-Slope Intercept Form- y = mx + b

Steps : 

Steps Find Slope Put the information into the y=mx + b form Remember: m= slope Replace x, y, and m with appropriate data points given.

Example : 

Example Data set: (4, 1) (5, 4) Slope = 3 Find ‘b’ by taking point (4,1). Plug 4 into x, 1 into y and 3 into m The equation should look like 1= 3(4) + b Solve for b b = -11

Identifying m and b in a given equation : 

Identifying m and b in a given equation If you are given a equation that is not in slope intercept form you need to use functions of math to put the equation into that form Ex. -x + 2y= 12 Add x from each side 2y= x +12 Divide by two on each side of the equation. y= 1/2 x +6 Now your equation is in y= mx+b form. M is the slope b is the y intercept

Parallel Lines : 

Parallel Lines A parallel line must have the same slope as the original equation. They need to have a different y intercept. Ex. Y = 1/2 x + 6 Parallel line is Y= 1/2 x + b where b is less or greater than 6. Common mistakes are forgetting that b can be any number but the original equation

Parallel lines : 

Parallel lines There are also more advance equations such as find the line parallel to 2x-3y = 12 that goes through the point (1,7) The first step is to get your equation into slope intercept form y = 2/3x -4 You know the slope has to be the same but the y intercept has to a certain number because the line must go through (1,7) Plug in for x y and m in the new equation. 7= 2/3(1) + b Then solve. 7/.666= 10.5 b= 10.5 Your new equation is y = 2/3x + 10.5

Perpendicular lines : 

Perpendicular lines A perpendicular line has a slope that is the opposite reciprocal as the original equation. Ex. ½ and -2 The Y intercept can be any number. Ex. Y = 1/2 x + 6 Perpendicular line is Y= -2x + any number A common mistake is forgetting to change the sign.

Perpendicular lines : 

Perpendicular lines There are also more advance equations for perpendicular lines such as find the slope perpendicular to a line with points at (1,6) and (-2, 3) First step is to find the slope using y/x the slope is 1 Find the opposite reciprocal -1 is the slope

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