Question

Which equation represents a linear function?

Equation 1: y = 2x2 + 1
Equation 2: y2 = 8x + 1
Equation 3: y = 5x3 – 1
Equation 4: y = 7x – 1
Equation 1 Equation 2 Equation 3 Equation 4

Answer 1

the numbers after the variables are exponents

Answer 2

linear functions don't have exponents. Which is that?

Answer 3

equation 4

Answer 4

i have more questions

Answer 5

Brian and Cyril spend a certain amount of money from their money box each month to buy plants.

The table shows the relationship between the amount of money (y) remaining in Brian's money box and the number of months (x):

Function 1:

Number of Months
(x) Amount Remaining (dollars)
(y)
1 65
2 59
3 53
4 47


The equation shows the relationship between the amount of money, y, remaining in Cyril's money box and the number of months, x.

Function 2:
y = –8x + 65

Which statement explains which function shows a greater rate of change?

Function 2 shows a greater rate of change, because Cyril spends $8 each month and Brian spends $6 each month. Function 2 shows a greater rate of change, because Cyril spends $65 each month and Brian spends $18 each month. Function 1 shows a greater rate of change, because Brian spends $18 each month and Cyril spends $57 each month. Function 1 shows a greater rate of change, because Brian spends $6 each month and Cyril spends –$8 each month.

Answer 6

@peachpi

Answer 7

use the slope formula to find the rate of change for function 1
\[m=\frac{ y_2-y_1 }{ x_2-x_1}\]
Pick any two points to plug in

Answer 8

1 and 65

Answer 9

you can use 1 for x_1 and 65 for y_1. Now pick another point for x_2 and y_2.

Answer 10

Then plug them into the formula

Answer 11

i dont understand

Answer 12

@perl

Answer 13

Each pair of numbers in that table represent a point on a line. They're asking you to find the slope of the line that has the points (1, 65), (2, 59), (3, 53), and (4, 47). Does that make sense?

Answer 14

yes

Answer 15

function 2 has a rate of change of 8, am i right?

Answer 16

-8

Answer 17

but the change is by 8, negative or not

Answer 18

Do you understand how to get the rate of change for function 1?

Answer 19

no

Answer 20

not really. the direction matters. ROC of 8 means the function is increasing. ROC of -8 means it's decreasing

Answer 21

btw these are the answer choices:

A: Function 2 shows a greater rate of change, because Cyril spends $8 each month and Brian spends $6 each month.

B: Function 2 shows a greater rate of change, because Cyril spends $65 each month and Brian spends $18 each month.

C: Function 1 shows a greater rate of change, because Brian spends $18 each month and Cyril spends $57 each month.

D: Function 1 shows a greater rate of change, because Brian spends $6 each month and Cyril spends –$8 each month.

Answer 22

For function 1 let's just consider the 2 points (1, 65) and (2, 59). This is how you put them into the slope equation