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