Download Finding the Rate of Change (Slope)

Algebra I
Finding the
Rate of Change (Slope)
January 3, 2013
But first,
New seating charts!!!!!!!!!!
Introduction…..
DefinitionsSlope- The ratio of the vertical change to the
horizontal change.
Also known as the Rate of Change.
Finding Slope given
Standard Form or Slope-Intercept Form
Standard Form- Ax + By = C
Slope-Intercept Form- y = mx + b
Step 1: Solve the equation for y (if not already).
Step 2: Slope is always the coefficient of x.
Coefficient- The numerical factor when a term has a
variable.
In other words, it is the number directly beside the
variable (letter).
Such as 3 is the coefficient of 3x
Finding Slope given
Standard Form or Slope-Intercept Form
Example:
Find the slope of the following linear equation
y = 6x + 4
Step 1: Solve the equation for y.
This linear equation is already solved for y because y is on
one side of the equal sign by itself.
Step 2: Slope is the coefficient of x.
The coefficient of x in this equation is 6. Therefore, the
slope of this linear equation is 6.
Finding Slope given
Standard Form or Slope-Intercept Form
Example:
Find the slope of the following equation
15 – ⅗x = y
Step 1: Solve the equation for y.
This equation is already solved for y because y is on one
side of the equal sign by itself.
Step 2: Slope is the coefficient of x.
The coefficient of x is -⅗. Therefore, the slope of
this linear equation is -⅗.
Finding Slope given
Standard Form or Slope-Intercept Form
Example:
Find the slope of the following equation
4x – 2y = 16
Step 1: Solve the equation for y.
This equation is not already solved for y. So we need to
solve this equation for y. When we do this, we will get
the equation y = -8 + 2x
Step 2: Slope is the coefficient of x.
The coefficient of x is 2. Therefore, the slope of this
linear equation is 2.
Finding Slope given
Standard Form or Slope-Intercept Form
Try the following problems on your own.
Find the slope of the following linear equations.
1.
2.
3.
4.
5.
4x + 6 = y
5 - ¼x = y
2x – 5 = y
2y = 5x + 3
-4x + 2y = 10
Finding Slope given
Standard Form or Slope-Intercept Form
Try the following problems on your own.
Find the slope of the following linear equations.
1.
2.
3.
4.
5.
6x + 8y = 12
-⅓x + 3 = 5y
6x = 3y + 15
Challenge: y = -3
Challenge: x = -4
Finding Slope given
the graph of the line.
When given the graph of a linear equation, you
can pick any two points and create a right
triangle connecting the two points. This is
called the slope triangle. When you count the
rise and run you will find the slope or the rate
of change.
Finding Slope given
the graph of the line.
Finding Slope given
the graph of the line.
Exit Slip!
Find the slope of the line given the following
equations.
1. -8x + 2y = 10
2. y = -2x + 4
Find the slope of the lines graphed on the
coordinate plane below.
4.
3.
3.
4.