Algebra 1 Common Core Student Edition, Grade 8-9

How do you identify
the y-intercept?
The y-intercept is the
y-value when x = 0.
So the y-intercept is the
pressure at a depth o f
0 m.This is the starting
value, 1 atm.

S lope-intercept form is useful for m odeling real-life

situations w here you are given a starting value (the

y-intercept) a n d a rate of change (the slope).

Pr o b l em 6 Modeling a Function

Physics Water pressure can be measured in

atmospheres (atm ). Use the information in the

diagram to write an equation that models the

pressure y at a depth of x m e t e r s. W h a t g ra p h

models the pressure?

Step 1 Identify th e slope a n d th e y-intercept.

The slope is th e rate of change, 0.1 a tm /m.

The y-intercept is the starting value, 1 atm.

Step 2 Substitute th e slope an d y-in tercep t into the

slope-intercept form.

y = m x + b Use slo p e -in te rc e p t form ,

y = O.lx + 1 Substitute 0.1 for m and 1 for b.

Step 3 Graph the equation.

The y-intercept is 1. Plot th e p o in t (0,1).

The slope is 0.1, w hich equals -p,. Plot a

second p o in t 1 u n it above an d 10 u n its to

th e right of th e y-intercept. Then draw a

line through th e two points.

Go t I t? 6. A p lu m b er charges a $65 fee for a repair

plus $35 p e r hour. W rite an eq u a tio n to

m odel th e total cost y of a re p air th a t takes

x hours. W hat graph m odels th e total cost?

Pressure Underw ater

Lesso n Ch eck

Do y o u k n o w H OW?

1. W hat is an e q u a tio n of th e line w ith slope 6 a n d
   y-intercept -4?


2. W hat equation in slope-intercept form represents
   the line th a t passes through th e points
   (-3,4) and (2,-1)?


3. W hat is th e graph of y = 5x + 2?

MATHEMATICAL

Do y o u UN DERSTAND? J g J PRACTICES

4. Vocabulary Is y = 5 a linear equation? Explain.


5. Reasoning Is it always, sometimes, or never t r u e t h a t
   a n equation in slope-intercept form represents a
   direct variation? Support your answ er w ith examples.


6. W r i t i n g D escribe two different m eth o d s you can use
   to graph th e eq u a tio n y = 2x + 4. W hich m eth o d do
   you prefer? Explain.

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PowerAlgebra.com Lesson 5-3 Sl o p e - l n t e r c e p t Fo r m^311