Download y = mx + b

Lesson 4.1
Essential
Question #1
Writing Equations in Slope-Intercept
Form
Given a y-intercept & a slope can you write
the equation of the line?
You have a slope of -3 and a y-intercept of 4. What is the slope-intercept
equation?
Slope-Intercept formula: y = m x + b
Substitute “-3” for m and “4” for b
y = (-3) x + (4) or in function form f(x) = -3 x + 4
You try:
slope: 2
Y-intercept: 9
slope: -3
Y-intercept: 0
y = 2x + 9
y = -3 x
In function form:
In function form
f(x) = 2x + 9
f(x) = -3 x
Essential
Question #2
Given the graph of a linear function, how
can you write the equation of the line?
What is the slope of the line?
(2,2)
m=
Y2 – Y1
X2 – X1
=
2 – (-2)
2 – (0)
=
4
=
2
2
What is the y-intercept of the line? (0,-2)
(0,-2)
Can you write a function for this line in slope
intercept form and if so what is the function?
y = mx+b or y = 2 x - 2
or in function form f(x) = 2 x - 2
Essential
Question #3
Given two points can you write the equation
of the line?
Step 1: Find the slope.
m=
Y2 – Y1
X2 – X1
Step 2: Find the y-intercept. Substitute the slope m and the
coordinates of one of the points into the slope-intercept form,
y = mx + b, and solve for the y-intercept b.
Step 3: Write an equation of the line. Substitute the slope m and the
y-intercept b into the slope-intercept form, y = mx + b.
EXAMPLE
Write an equation of the line that passes through the points (1, -3) and (3, 5).
(x2,y2)
(x ,y )
1
1. Find the slope. m=
5 – (-3)
m=
8
m=4
3–1
2
2. Find the y-intercept. Choose one of the ordered pairs.
(Either ordered pair will result in the same y-intercept)
Using (1, -3)
Using (3, 5)
y = mx + b
y = mx + b
-3 = 4(1) + b
-3 = 4 + b
-4 -4
-7 = b
5 = 4(3) + b
5 = 12 + b
-12 -12
-7 = b
1
EXAMPLE (continued)
3. Substitute the slope and the y-intercept into
m=4
and
EXAMPLE
y = mx + b
y = 4x - 7
b = -7
You try:
1. Find the equation of a line passing through the points
(1, 6) and (3, -4).
Steps
1) Find slope
m=
(-4) – (6)
m = -5
3–1
2) Find y-intercept b
(6) = -5 (1) + b
b = 11
3) Write equation
Y = -5x +11 or f(x) = - 5 x + 11 (in function form)
Essential
Question #4
Vocabulary
Given real-life problem, how do you model
using mathematics the equation of the line?
Linear Model – a linear function that models a real-life situation
A camp program charges a registration fee and a daily amount. If the total bill for
one camper was $338 for 12 days and the total bill for another camper was $506
for 19 days, how much will the bill be for a camper who enrolls for 30 days?
Identify the independent variable (x) and the dependent variable (y).
Since part of the bill depends on the number of days, the independent variable
is the number of days.
Write the two ordered pairs. (12, 338) and (19, 506)
The registration fee is the y-intercept (b). This value is not known.
Steps
1) Find slope
2) Find y-intercept b
3) Write equation
Find the slope and the y-intercept.
(12, 338)
(19, 506)
m=
506 – 338
19 – 12
m=
168
7
m = 24
y = mx + b
338 = 24(12) + b
338 = 288 + b
-288 -288
y = 24x + 50 - This means that the camper pays
$24 each day and a registration
fee of $50.
50 = b
If a camper is there for 30 days, find the cost.
y = 24(30) + 50
y = 720 + 50
y = $770
Write a summary of what you have learned in this lesson