Download 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.
c)
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)
d)
e)
f)
b)
Slope Intercept Word Problems:
Ex 4:
Rewrite the following equations into slope intercept form
*solve for y*
y  mx  b
m: Slope
b: y-intercept
a) x  3 y  9
b) 4 x  6 y  8
c) 3 x  2 y  15
d) y  6  2( x  2)
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.
e) y  3  
2
( x  6)
3
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) x 
2
y 1
3
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) y  5  
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.
7 1
 ( x  4)
2 2
Practice:
i. Rewrite the following equations into slope
intercept form.
a) x  y  3
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.
f) y 
2
( x  15)
3
b)
1
x y4
2
d) y  2  3( x  1)
f) y 
3
1

 4 x  
5
2

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