- The document outlines notes on slope and linear equations from a class. It includes definitions of slope, formulas for calculating slope between two points, and examples of finding the slope and equation of a line from graphical data or given information. - Students will review slope formulas, work examples and practice problems, and complete class work 2.11 applying concepts of slope and linear equations. The notes provide guidance on finding slope, writing equations of lines in slope-intercept and standard form, and graphing lines on coordinate planes.

1. Today:
 No Warm-Up
 Review Slope & Other Formulas
 Examples & Practice
 Class Work 2.11

2. (Class Notes Section of Notebook)

3. Y is the dependent variable.
X is the independent variable.
The constant rate of change of a line is called
the slope of the line.
The rise is the difference of the y-values of two
points on a line.
The run is the difference in the x-values of
two points on a line.
The slope of a line is the ratio of rise
to run for any two points on the line.
change in y
change in x
Rise
Run
=
Slope Sense

4. (3, 2)
(–1, –2)
Then count horizontally to a
second point to find the run.
Count vertically from any
one point on the line to
find the rise.
Finding the Slope of a Line
slope= = 14
4
The slope of the line is 1.
–4
–4slope = = 1
It does not matter which
ordered pair you start with.
Slope Sense

5. Then count horizontally to a
second point to find the run.
Count vertically from any one
point on the line to find the rise.
slope = =2
4
1
2
The slope of the line is -
1
2
–2
–4
slope = = 1
2
(5, 4)
(1, 2)
Slope Sense

6. Slope Sense
What is the equation of this line?
The point here, is called the....
y-intercept. We know the
slope, so we can plug both into
the slope-intercept form of a
line and get.... y = 2/3x - 2

7. Slope Sense

8. What is the slope of the line?
Slope Sense

9. Slope Sense
Which slope, or grade, is the steepest? Why?
𝟏𝟕
𝟏𝟎𝟎
=
𝒙
𝟓𝟎𝟎 x = 85
𝟐𝟓
𝟓𝟎𝟎
=
𝟓
𝟏𝟎𝟎
***A line is straight ONLY because the slope is
the same throughout the entire line

10. Use graph paper and label the axes with the following values:
A car rental agency charges $25/day to rent a
compact car, and $50/day to rent a sports car.
For each car, graph the cost of renting for 1
to 3 days. Plot the points and connect with a
continuous line graph.
cost
days 1 2 3
y2 – y1
x2 – x1
m =
Slope measures how y changes, given a
change in x (which must come first).
In other words, “How will a change in our
independent variable affect the dependent
variable?
change in y
change in x
Over the same change in x, (3 days)
It’s easy to see that the sports car had
a greater affect on the ‘y’ (cost)...
Than the compact car, over the same change in x.
The steeper the line, the greater the change in y.
Slope Sense

11. Example:
The table shows the total cost of gas per gallon. Use the data to
make a graph. Find the slope of the line and explain what it shows.
Graph the data.
Cost of Gas
Gallons Cost
0 0
3 6
6 12
6
9
9
12
60
3
3 x
y
Gallons
Cost of Gas
Cost
0
Slope Sense

12. Example Continued
Find the slope of the line:
The slope of the line is 2. This means that for
every gallon of gas, you will pay another $2.
=
y2 – y1
x2 – x1
6
3
=
12 – 6
6 – 3
= 2
Slope Sense

13. Find the equation of the line that has a slope of
𝟏
𝟒
and a y-
intercept of 2. Graph the line and write the equation in both
slope-intercept and standard forms with integers only.
The Graph
The Equations
1. Slope-intercept form: The instant equation, just add x and y.
Fractional form: y =
𝟏
𝟒
x + 2 Integer form form: 4y = x + 8
2. Standard Form: Easily & directly found by doing this:
cross-multiply
The Other Formulas

14. Find the equation of the line that has a slope of 𝟑 and a y-
intercept of -1. Graph the line and write the equation in both
slope-intercept and standard forms with integers only for the
standard form.
On Your Own:
What if:
The only information you have is the slope
𝟑
𝟒
, and a point on the
line, (1,2). Use the correct equation & graph the line. Then write the
equation standard form with integers only.
You begin with the point-slope formula,
which becomes the slope-intercept form.
Use the slope-intercept to graph.
To put the equation in standard form,
you can do this...

15. Class Work 2.11;
Show All Work