Question

charter school
name
date
tables, equations, and graphs

1. given the table. write the equation. graph it!

initial value (start) =
rate of change =
( y = )

( x )	( y )
1	1
2	4
3	7

1. given the graph. write the equation.

slope =
( y )-intercept =
( y = )

1. given the equation. fill in the table.

( y = 5x - 12 )

( x )	( y )
-1
0
1
2
3
20

slope (rate of change)

1. find the slope

time (seconds)	profit (dollars)
9	25
12	29

( m = )

1. find the slope, ( x )-intercept, and ( y )-intercept.

( m = )
( b = )

1. find the slope of the line that contains the points:

( (-12, 8) ) and ( (-21, -20) )

1. bob has saved 32 gummi bears. his mom gives him 3 gummis every 2 days.

what is the rate of change?

Explanation:

Step1: Find initial value (y-intercept)

Initial value is $y$ when $x=0$: $b=-2$

Step2: Calculate rate of change (slope)

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}=\frac{1-(-2)}{1-0}=3$

Step3: Write linear equation

$y=mx+b$ → $y=3x-2$
---

Step1: Identify slope from graph

Use two points $(-4,8)$ and $(0,2)$: $m=\frac{2-8}{0-(-4)}=\frac{-6}{4}=-\frac{3}{2}$

Step2: Find y-intercept

y-intercept is $y$ at $x=0$: $b=2$

Step3: Write linear equation

$y=mx+b$ → $y=-\frac{3}{2}x+2$
---

Step1: Substitute $x=-2$ into equation

$y=5(-2)-12=-10-12=-22$

Step2: Substitute $x=-1$ into equation

$y=5(-1)-12=-5-12=-17$

Step3: Substitute $x=0$ into equation

$y=5(0)-12=0-12=-12$

Step4: Substitute $x=1$ into equation

$y=5(1)-12=5-12=-7$

Step5: Substitute $x=2$ into equation

$y=5(2)-12=10-12=-2$

Step6: Substitute $x=3$ into equation

$y=5(3)-12=15-12=3$

Step7: Substitute $x=20$ into equation

$y=5(20)-12=100-12=88$
---

Step1: Calculate slope from table

$m=\frac{25-21}{9-6}=\frac{4}{3}$
---

Step1: Calculate slope from graph

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

Step2: Find y-intercept

y-intercept is $y$ at $x=0$: $b=-3$

Step3: Find x-intercept

Set $y=0$: $0=\frac{3}{2}x-3$ → $\frac{3}{2}x=3$ → $x=2$
---

Step1: Calculate slope with two points

Slope formula: $m=\frac{y_2-y_1}{x_2-x_1}=\frac{-20-8}{-21-(-12)}=\frac{-28}{-9}=\frac{28}{9}$
---

Step1: Identify rate of change

Rate is gummis per day: $\frac{3}{2}=1.5$

Answer:

1. Initial value (start) = $\boldsymbol{-2}$; Rate of Change = $\boldsymbol{3}$; $y=\boldsymbol{3x-2}$

(Graph: Plot points $(0,-2),(1,1),(2,4),(3,7)$ and draw a straight line through them)

1. slope = $\boldsymbol{-\frac{3}{2}}$; y-intercept = $\boldsymbol{2}$; $y=\boldsymbol{-\frac{3}{2}x+2}$

3.

$x$	$y$
-1	-17
0	-12
1	-7
2	-2
3	3
20	88

1. $m=\boldsymbol{\frac{4}{3}}$
2. $m=\boldsymbol{\frac{3}{2}}$; x-intercept = $\boldsymbol{2}$; y-intercept ($b$) = $\boldsymbol{-3}$
3. $m=\boldsymbol{\frac{28}{9}}$
4. Rate of change = $\boldsymbol{\frac{3}{2}}$ (or 1.5) gummi bears per day