1. Using Equations in Standard and Slope Intercept Form

2. Standard Form: Ax + By = C
Remember:
Standard Form: Ax + By = C
A (the leading coefficient) must be positive
A, B and C must be integers
A, B and C will be numbers
x and y are the variables
Use standard form when you have two independent quantities

3. 9x + 7.5y = 40.50 90x + 75y = 405 90(2) + 75y = 405 and solve
Your family is going to see the new Star Wars movie. Adult tickets are $9 and child tickets are $ Your mom, step-dad, and siblings went and they spent $40.50 total on tickets.
Let x = adult tix and y = child tix
9x + 7.5y = 40.50
Since we are using standard form, we will multiply through by 10 to clear out decimals.
90x + 75y = 405
How many kids went?
90(2) + 75y = 405 and solve
y = 3, 3 kids went

4. You have $6. 00 to use to buy apples and bananas. If bananas cost $
You have $6.00 to use to buy apples and bananas. If bananas cost $.50 per pound, and apples cost $.30 per pound, write an equation that represents the different amounts of each fruit you can buy
Let x = bananas and y = apples
.50x + .30y = 6
Since we are using standard form, we will multiply through by 100 to clear out decimals.
50x + 30y = 600
Apples
x-intercept (12, 0)
I could buy 12 bananas and no apples for $6
y-intercept (0, 20)
I could buy 20 apples and no bananas for $6
Or I could buy a few of each as long they total $6 which is represented by all points on the line!
Bananas

5. Slope Intercept Form: y = mx + b
Remember:
Slope Intercept Form: y = mx + b
-Use slope Intercept form when you know (or can calculate) a rate of change
-Use if you have an independent and dependent quantity

6. Real-life application
Between 1980 and 1990 the number of vacations taken by Americans increased by about 15,000,000 per year.
In 1985 Americans went on 340,000,000 vacation trips.
Find an equation that gives the number of vacation trips, y (in millions), in terms of years, t.

7. A Linear Model for Vacation Travel
Solution
It is your rate of change.
The constant rate is 15 million trips/year, so
m= 15
(5, 340)
Where 5 represents 1985
340 represents the number of trips in millions
Question
What is your slope?
What is your given point?

8. So the slope-intercept form of the
Now follow the steps and find the equation when m = 15 and the given point is (5, 340)
Follow the steps:
y = mx + b
340 = 15(5) + b (plug in m, x, and y)
340 = 75 + b (subtract 75 from both sides)
265 = b
y= 15x (plug in the m and b value)
So the slope-intercept form of the
equation is y=15t+265