Question

taking with vocabulary (continued)
in exercises 12 and 13, graph the linear function.

1. $s(x) = \frac{1}{2}x - 2$
2. $t(x) = 1 - 2x$

$x$	$-4$	$-2$	$0$	$2$	$4$
$s(x)$
$x$	$-2$	$-1$	$0$	$1$	$2$
$t(x)$

(graphs with coordinate planes for plotting)

1. the function $b(m) = 50m + 150$ represents the balance (in dollars) in your savings account after $m$ months. the table shows the balance in your friend’s savings account. who has the better savings plan? explain.

month	balance
2	$330
4	$410
6	$490

Explanation:

Exercise 12:

Step1: Calculate \( s(x) \) for each \( x \)

For \( x = -4 \): \( s(-4)=\frac{1}{2}(-4)-2=-2 - 2=-4 \)
For \( x = -2 \): \( s(-2)=\frac{1}{2}(-2)-2=-1 - 2=-3 \)
For \( x = 0 \): \( s(0)=\frac{1}{2}(0)-2=0 - 2=-2 \)
For \( x = 2 \): \( s(2)=\frac{1}{2}(2)-2=1 - 2=-1 \)
For \( x = 4 \): \( s(4)=\frac{1}{2}(4)-2=2 - 2=0 \)

Step2: Plot the points

Plot the points \((-4, -4)\), \((-2, -3)\), \((0, -2)\), \((2, -1)\), \((4, 0)\) on the given graph and draw a line through them.

Table for \( s(x) \):

\( x \)	-4	-2	0	2	4

Exercise 13:

Step1: Calculate \( t(x) \) for each \( x \)

For \( x = -2 \): \( t(-2)=1-2(-2)=1 + 4=5 \)
For \( x = -1 \): \( t(-1)=1-2(-1)=1 + 2=3 \)
For \( x = 0 \): \( t(0)=1-2(0)=1 - 0=1 \)
For \( x = 1 \): \( t(1)=1-2(1)=1 - 2=-1 \)
For \( x = 2 \): \( t(2)=1-2(2)=1 - 4=-3 \)

Step2: Plot the points

Plot the points \((-2, 5)\), \((-1, 3)\), \((0, 1)\), \((1, -1)\), \((2, -3)\) on the given graph and draw a line through them.

Table for \( t(x) \):

\( x \)	-2	-1	0	1	2

Exercise 14:

Step1: Find the slope of friend's savings

The friend's balance data: \((2, 330)\), \((4, 410)\), \((6, 490)\)
Slope \( m_{friend}=\frac{410 - 330}{4 - 2}=\frac{80}{2}=40 \)

Step2: Compare slopes

Your savings function: \( B(m)=50m + 150 \), slope \( m_{you}=50 \)
Since \( 50>40 \), your savings plan has a greater rate of increase (slope), so you have a better savings plan.

Answer:

You have the better savings plan because the slope of your savings function (\( 50 \)) is greater than the slope of your friend's savings ( \( 40 \) ), meaning you save more per month.