Compare Linear Function 1 with Linear Function 2. Which one has the lesser rate of change? Choose 1 for Linear Function 1; choose 2 for Linear Function 2.

Question

Linear Function 1: y=7x+4
Linear Function 2:
x y
10 61
12 73

Answer 1

To compare the rate of change for linear functions, we need to find the slope or coefficient of the x-term in the equation.

Linear Function 1 is y = 7x + 4. The coefficient of the x-term is 7, so the rate of change for Linear Function 1 is 7.

Linear Function 2 is given with two points: (10, 61) and (12, 73). We can find the rate of change (slope) by using the formula: (change in y)/(change in x).

(change in y) = 73 - 61 = 12
(change in x) = 12 - 10 = 2

The rate of change for Linear Function 2 is 12/2 = 6.

Comparing the two rates of change, Linear Function 1 has a greater rate of change than Linear Function 2. Therefore, the lesser rate of change is for Linear Function 2.

Answer 2

Compare Linear Function 1 with Linear Function 2. Which one has the greater initial value? Choose 1 for Linear Function 1; choose 2 for Linear Function 2.
Linear Function 1: Taesha starts the year with $50 saved and then saves an additional $25 a week.
Linear Function 2: The relationship between the number of weeks Joshua has been saving (x) and his total savings (y) is given by y=37x+40

Answer 3

To compare the initial value of the two linear functions, we need to look at the y-intercept or the value of y when x is equal to 0.

For Linear Function 1, the equation is y = 25x + 50. When x is 0, y = 25(0) + 50 = 50. The initial value is $50.

For Linear Function 2, the equation is y = 37x + 40. When x is 0, y = 37(0) + 40 = 40. The initial value is $40.

Comparing the initial values of the two linear functions, Linear Function 2 has a greater initial value. Therefore, the answer is 2 for Linear Function 2.