Learning Goal #1 for Focus 4
(HS.A-CED.A.2, HS.REI.ID.10 & 12, HS.F-IF.B.6, HS.F-
IF.C.7, HS.F-LE.A.2):
The student will understand that linear relationships can be described using multiple representations.
4
In addition to level 3.0 and above and beyond what was taught in class, the student may:
· Make connection with other concepts in math
· Make connection with other content areas.
3
The student will understand that linear relationships can be described using multiple representations.
- Represent and solve equations and inequalities graphically.
- Write equations in slope-intercept form, point-slope form, and standard form.
- Graph linear equations and inequalities in two variables.
- Find x- and yintercepts.
2 1 0
The student will be able to:
- Calculate slope.
- Determine if a point is a solution to an equation.
- Graph an equation using a table and slopeintercept form.
With help from the teacher, the student has partial success with calculating slope, writing an equation in slopeintercept form, and graphing an equation.
Even with help, the student has no success understanding the concept of a linear relationships.

•Slope is the change in y over change in x.
•Slope is represented by the letter m
•Vertical line has NO slope
•Horizontal line has a slope zero (0)

m
 y
2 x
2

 y x
1
1
= rise
= run
 y
 x

m


3
2


1
1


3
2

A slope of 3 /
2 means that or every time y goes down 3, x moves right 2
Graph and count to check.
4
3
2
1
-4 -3 -2 -1 -1 1 2 3 4
-2
-3
-4

y x
1. A line with a positive slope rises from left to right (m>0)

2. A line with a negative slope falls down from left to right (m<0) y x

3. A line with a zero slope is horizontal (m=0) Equation y = 3 y x

4. A line with an undefined slope is vertical
(m is undefined) YOU CANT DIVIDE BY 0!
y x

RATE OF CHANGE:
At 3:00 p.m. a car leaves the city. By 5:00 it has traveled 90 miles. Find its average speed.
Change in miles
Change in time(hours)

90

0
Notice you have two pairs:

5

3
45 mph
(3,0) and (5,90)
Where x is time and y is miles.

The temp. is 63 F at 7a.m. By
10a.m., its 45 F. Find the average rate of change in temp.
Change in temp
Change in time
Two pairs:
(7,63) and (10,45)



63
7
18
3


45
10
= -6 degrees per hour

Find the value of y for the line going through points (-3, -2), (1, y ) when the slope of the line is 2
2 = y - -2
1 - -3
2 = y + 2
4
8 = y + 2
6 = y