5-3 Slope Intercept Form
Common Core Math 1
Day 3 – Classroom Notes – Slope-intercept Form
I. Writing Linear Equations
Note: If I say draw a picture of your Mom. It is the same as me asking you to draw the graph of a linear equation.
A linear equation is like a name of a person.
A linear equation is a _______ of a line.
Slope is like saying a person is fat/skinny, tall/short, etc..
Slope is a ____________ term.
Slope Intercept Form: (y= form)
*Most famous of all forms of linear equations
y=(Pattern)x + (Starting Point) y=(coefficient)x + (constant term)
y = (Slope)x + (y-intercept)
y = mx + b
m = slope y-intercept (0, b)
Ex1: Write an equation given the slope and the y-intercept.
a) Slope is 3 and y-intercept is 5
b) Slope is -2 y-intercept is -7
c) m = -3 and b = 4
d) m = 5 and b = -1
Ex2: Write an equation of a line given a graph.
a)
[pic]
b)
[pic]
c)
[pic]
d)
[pic]
e)
[pic]
f)
[pic]
Slope Intercept Word Problems:
[pic]
m: Slope b: y-intercept
Ex 3:
Write the function rule for the following word problems in Slope – Intercept Form.
1) You rent a bicycle for $20 plus $2 per hour
2) An auto repair shop charges $50 to diagnose the problem plus $25 per hour to repair it.
3) A candle is 6 inches tall and burns at a rate of ½ inch per hour.
4) Temperatures on January 13, 2015 where 15 degrees and were expected to fall 2 degrees per hour throughout the night.
Practice: Word Problems.
Solve:
a) To rent a canoe you must pay an initial fee of $25 plus $10 per hour. Create the function rule in slope-intercept form and describe the slope and y-intercept.
b) Ms. Hernandez’s car broke down. ( The auto repair shop uses the following equation as a way to charge customers C = 50 + 25h. Explain the function rule.
c) A candle is 12 inches tall and burns at a rate of 2 inches per hour. Create the function rule in slope-intercept form and describe the slope and y-intercept.
d) A computer is purchased for $1,200 and depreciates at $140 per year. Write a linear equation that represents the value , V, of the computer at the end of t years?
e) Jim is selling hot dogs at a ball game. It cost Jim $250 to purchase everything to make hot dogs. Jim sells hot dogs for $2 each. If he sells h hot dogs, write an equation that models his profit.
Ex 4:
Rewrite the following equations into slope intercept form *solve for y*
a) [pic] b) [pic]
c) [pic] d) [pic]
e) [pic] f) [pic]
Practice:
i. Rewrite the following equations into slope intercept form.
a) [pic] b) [pic]
c) [pic] d) [pic]
e) [pic] f) [pic]
Homework:
Shayley just bought a new phone with a new minutes plan. She can calculate her phone bill using the following equation y = 0.10x + 35. What does the 0.10 represent? What does the 35 represent?
Suppose you have already saved $50 toward the cost of a new television set. You plan to save $5 more each week for the next several weeks. Write an equation for the total amount T you will have w weeks from now. Find the total amount saved after 7 weeks.
The following equation is used to determine the temperature T as the hours h go by at night T = -2h + 15. What does the -2 represent? What does the 15 represent?
To rent a bicycle it costs $20 plus $2 per hour. Write an equation to represent the cost of renting a bicycle
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