Question

the relationship between the x- and y- values in each table is linear. write a function. find the amount and rate of change. (5 & 6)

Answer 1

(5)

Since, the relationship is linear

so, we can use point slope form of line and find equation of line

we can select any two points

first point is (4,10)

so, x1=4 , y1=10

second point is (7,17.5)

so, x2=7 , y2=17.5

now, we can find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

now, we can plug values

$m=\frac{17.5-10}{7-4}$

$m=2.5$

now, we can use point slope form of line

$y-y_1=m(x-x_1)$

now, we can plug values

$y-10=2.5(x-4)$

we get

$y=2.5x$

Initial amount:

It is the value of y when x=0

so, we can plug x=0 and find y

$y=2.5\times 0$

$y=0$

So, initial amount is 0

Rate of change:

we know that rate of change is slope

so, m=2.5

so, the rate of change is 2.5

(6)

Since, the relationship is linear

so, we can use point slope form of line and find equation of line

we can select any two points

first point is (2,29)

so, x1=2 , y1=29

second point is (5,41)

so, x2=5 , y2=41

now, we can find slope

$m=\frac{y_2-y_1}{x_2-x_1}$

now, we can plug values

$m=\frac{41-29}{5-2}$

$m=4$

now, we can use point slope form of line

$y-y_1=m(x-x_1)$

now, we can plug values

$y-29=4(x-2)$

we get

$y=4x+21$

Initial amount:

It is the value of y when x=0

so, we can plug x=0 and find y

$y=4\times 0+21$

$y=21$

So, initial amount is 21

Rate of change:

we know that rate of change is slope

so, m=4

so, the rate of change is 4