Question

write a linear function that relates y to x. (see examples 1 and 2.)
1.
2.
3.

x	-3	0	3	6
y	3	5	7	9

4.

x	-8	-4	0	4
y	2	1	0	-1

1. test prep which equations are linear functions? select all that apply.

a ( y = -5x + 3 )
c ( x = 7 )
b ( y = 3 )
d ( 2x - 6y = 24 )

1. the table shows the length of a person’s hair after x months. (see example 3.)

a. write and graph a linear function that relates y to x.
b. interpret the slope and the y - intercept.

months, x	hair length (inches), y
0	11.0
3	12.5
6	14.0

1. the table shows the percent (in decimal form) of battery power on a tablet after x hours.

a. write and graph a linear function that relates y to x.
b. interpret the slope, the x - intercept, and the y - intercept.

hours, x	power remaining, y
0	1.0
2	0.6
4	0.2

1. connecting to real life the number y of calories burned after x minutes of kayaking is represented by ( y = 4.5x ). the graph shows the number of calories burned by hiking. (see example 4.)

a. which activity burns more calories per minute?
b. you perform each activity for 45 minutes. how many total calories do you burn?

Explanation:

Problem 1

Step1: Identify slope and intercept

The line is horizontal, so slope $m=0$, $y$-intercept $b=3$.
Linear function form: $y=mx+b$

Step2: Substitute values

$y = 0x + 3$

Step1: Calculate slope

Use points $(0,3)$ and $(2,7)$: $m=\frac{7-3}{2-0}=2$

Step2: Identify y-intercept

$b=3$ (when $x=0$, $y=3$)

Step3: Write function

$y=mx+b$

Step1: Calculate slope

Use points $(0,5)$ and $(3,7)$: $m=\frac{7-5}{3-0}=\frac{2}{3}$

Step2: Identify y-intercept

$b=5$ (when $x=0$, $y=5$)

Step3: Write function

$y=mx+b$

Answer:

$y=3$

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Problem 2