1. Unit 7 More Functions: LT 7.1B - Solving for y
Solving for y is just like solving for x when we were finding solutions for equations Since we are solving, you will use the order of operations backwards.

2. Easy Examples Positive 1y
3x + y = 12 Move 3x by subtraction -3x -3x y = -3x + 12 Put the x first number last
You Try 4x + y = 1 4x + y = 1 -4x -4x y = -4x + 1

3. Little Harder Negative y
3x - y = 12
Move -y by adding y
+y y
3x = y + 12
Subtract 12
3x -12 = y
You try 5x - y = 10 + y +y 5x = y x -10 = y

4. Day 2 Coefficient with y Positive with your y, don’t move it
3x + 4y = 12
4y = -3x + 12
Divide everything by 4
4𝑦 4 = −3𝑥
y = −3 4 x + 3
Negative with y, move it 5x - 20y = 40 5x = 20y x – 40 = 20y Divide everything by 20 5𝑥 20 −40 20 = 20𝑦 x - 2 = y

5. Hardest Fraction in initial problem and y is not 1 or -1
3 5 x - 2y = 4
Multiply everything by the denominator
5( 3 5 x - 2y = 4)
3x – 10y = 20
3x – 20 = 10y 3𝑥 10 −20 10 = 10𝑦 10 y = 3 10 x - 2

6. LT B2 Preview Graphing slope and y -intercept
Slope hasn’t changed m = 𝑢𝑝 𝑜𝑟 𝑑𝑜𝑤𝑛 𝑙𝑒𝑓𝑡 𝑡𝑜 𝑟𝑖𝑔ℎ𝑡 Lowercase b is used for the y – intercept.
The y-intercept is where a line crosses the y-axis. It is the point (0, y) or (0,b).

7. You need 2 points to graph a line
You need 2 points to graph a line. Which you have if you know the slope and y-intercept.
Example 1 Slope = −3 2 and y-int = 4 Graph the y intercept first.
Next from the y-intercept you the slope to find another point.

8. Graph a line with m = −1 4 and b = -2
First place the y-int on the graph
Now find the other point with the slope

9. Example 2 Slope of 3, and y-intercept is 6
Find the y-int (0,6) on a graph
Step 4 From that point, go up 3 and to the right 1. Connect points and cross both axes.

10. Graph the line with slope of 1 and y-int of -5
First put the point (0,-5) on a graph
From that point, go up 1 and to the right 1.

11. LT B2 Day 2 Graphing Lines in Slope-Intercept form y = mx + b
Steps in graphing a line from slope–intercept
Solve for y if needed
Name the slope (m) and y-intercept (b)
Find the y-intercept on the graph (0,b)
Use the slope to find one other point
Connect the points and name them, line should go through both axes.

12. Step 1 - solve for y -3x + y = 6 y = 3x + 6
Step 2 Name slope and y - intercept m = 3 and b = 6

13. Step 3 Find the y-int (0,6) on a graph
Step 4 From that point, go up 3 and to the right 1. Connect points and cross both axes.

14. Graph y = −2 5 x + 3
Find the slope and y-intercept m = −2 5 and b = (0, 3) Graph

15. Horizontal Line and Vertical Line Equations
Horizontal Line Equation
Slope = 0
y = c is the equation
y-intercept is always the constant
Example y = 3
Vertical Line Equation
Slope = undefined
x = c is the equation
There is no y-intercept
Example x = 3

16. Graph y = 4 and x = -3

17. LT 7.B3 I can construct functions from word problems. Day 1

18. Example 2

19. LT 7.B3 Day 2 Real Life Example from Budget Truck Rentals

20. Example

21. What is the initial cost for a 12’ foot truck for a day
What is the initial cost for a 12’ foot truck for a day? What is the rate of change ?
Initial Cost $43 Rate of Change .20 per mile

22. C = .20m + 43 C = .20(50) + 43 $53 Initial Cost $43
Can you write a function for that information? How much would it cost for one day and 50 miles?
Initial Cost $43
Rate of Change per mile
C = .20m + 43 C = .20(50) + 43 $53

23. What is the initial cost for a 16’ foot ramp truck for a day
What is the initial cost for a 16’ foot ramp truck for a day? What is the rate of change ?
Initial Cost $51 Rate of Change .20 per mile

24. Can you write a function for that information
Can you write a function for that information? How much for one day and 100 miles?
Initial Cost $51
Rate of Change per mile
C = .20m + 51 C = .20(100) + 51 $71

25. One More, what happens if you are not giving the initial amount?
Miles
Cost 1 75 2
100 3
125 4
150
The initial amount is the y - intercept. If you went back to 0 miles could you find the cost? $50 What is the rate of change? $25 per mile Function?? F(c) = 25m + 50

26. 7. 4B 1. Which linear function has the greatest slope
7.4B 1. Which linear function has the greatest slope? Which linear function has the greatest y - intercept x y 3 1 4 2 5 6

27. 7. 4B 1. Which linear function has the greatest slope
7.4B 1. Which linear function has the greatest slope? Which linear function has the greatest y - intercept x y 2 1 5 8 3 11

28. 7. 4B 1. Which linear function has the greatest slope
7.4B 1. Which linear function has the greatest slope? Which linear function has the greatest y - intercept x y 1 4 2 8 3 12 16 x y 1 2 5 3 8 4 11

29. Day 2 Determine whether each graph, equation, or table represents a linear on nonlinear equation

30. Equations y = 3x + 5 Linear y = 2 𝑥 2 + 5x Nonlinear
x = 6 linear 7x + 5y = 8 𝑥+2 = 6 Nonlinear

31. Graphs