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.
Linear Function 1: y=7x+4
Linear Function 2:
x y
10 61
12 73
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.
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
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.
To compare the rate of change of Linear Function 1 and Linear Function 2, we need to examine the slope of each linear function. The slope represents the rate of change in the y-values for every unit increase in the x-values.
Linear Function 1 is in the form: y = mx + b, where m is the slope. In this case, the slope of Linear Function 1 is 7.
Linear Function 2 is giving us a table of x and y values. We can find the rate of change by calculating the difference in y-values divided by the difference in x-values.
For Linear Function 2:
For the first set of points, the difference in y-values is 61 - 73 = -12, and the difference in x-values is 10 - 12 = -2. So, the rate of change is -12/-2 = 6.
For the second set of points, the difference in y-values is 73 - 61 = 12, and the difference in x-values is 12 - 10 = 2. So, the rate of change is 12/2 = 6.
Comparing the rates of change:
Linear Function 1 has a slope of 7, while Linear Function 2 has a rate of change of 6. Therefore, Linear Function 1 has a larger rate of change than Linear Function 2.
So, the answer is 1 (Linear Function 1).