The equation y=mx+b defines what type of function?(1 point)
Responses
a linear function
a linear function
an initial value function
an initial value function
a nonlinear function
a nonlinear function
a slope function
11 answers
a linear function
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Use the table to answer the question.
x y
6 16
15 43
Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y=mx+b form.
(1 point)
x y
6 16
15 43
Write the equation of the linear function that models the relationship shown in the table. Enter your answer in y=mx+b form.
(1 point)
To find the equation of the linear function that models the relationship shown in the table, we need to first determine the values of m (slope) and b (y-intercept).
Using the points (6, 16) and (15, 43):
Calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
m = (43 - 16) / (15 - 6)
m = 27 / 9
m = 3
Substitute one of the points into the equation y = mx + b to find the y-intercept (b):
16 = 3(6) + b
16 = 18 + b
b = 16 - 18
b = -2
Therefore, the equation of the linear function in y=mx+b form that models the relationship shown in the table is:
y = 3x - 2.
Using the points (6, 16) and (15, 43):
Calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
m = (43 - 16) / (15 - 6)
m = 27 / 9
m = 3
Substitute one of the points into the equation y = mx + b to find the y-intercept (b):
16 = 3(6) + b
16 = 18 + b
b = 16 - 18
b = -2
Therefore, the equation of the linear function in y=mx+b form that models the relationship shown in the table is:
y = 3x - 2.
Last year, Alayah ordered 4 cubic yards of soil and spent $220. This year, she orders 7 cubic yards of soil and spends $340. Write the equation of the linear function that models the relationship between the number of cubic yards of soil ordered and the total cost. Enter your answer in y=mx+b form.(1 point)
To write the equation of the linear function that models the relationship between the number of cubic yards of soil ordered and the total cost, we need to first find the values of m (slope) and b (y-intercept).
Using the points (4, 220) and (7, 340):
Calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
m = (340 - 220) / (7 - 4)
m = 120 / 3
m = 40
Substitute one of the points into the equation y = mx + b to find the y-intercept (b):
220 = 40(4) + b
220 = 160 + b
b = 220 - 160
b = 60
Therefore, the equation of the linear function in y=mx+b form that models the relationship between the number of cubic yards of soil ordered and the total cost is:
y = 40x + 60.
Using the points (4, 220) and (7, 340):
Calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
m = (340 - 220) / (7 - 4)
m = 120 / 3
m = 40
Substitute one of the points into the equation y = mx + b to find the y-intercept (b):
220 = 40(4) + b
220 = 160 + b
b = 220 - 160
b = 60
Therefore, the equation of the linear function in y=mx+b form that models the relationship between the number of cubic yards of soil ordered and the total cost is:
y = 40x + 60.
Compare Linear Function 1 with Linear Function 2. Which one has the greater rate of change? Choose 1 for Linear Function 1; choose 2 for Linear Function 2.
Linear Function 1: y=x+8
Linear Function 2:
A coordinate plane shows the x-axis ranging from negative 2 to 6 in increments of 1 and the y-axis ranging from negative 2 to 12 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 2 comma 6 right parenthesis and left parenthesis 4 comma 10 right parenthesis.
(1 point)
Linear Function
has the greater rate of change.
Linear Function 1: y=x+8
Linear Function 2:
A coordinate plane shows the x-axis ranging from negative 2 to 6 in increments of 1 and the y-axis ranging from negative 2 to 12 in increments of 1. A line with arrows at both ends joins two plotted points. The coordinates of the plotted points are as follows: left parenthesis 2 comma 6 right parenthesis and left parenthesis 4 comma 10 right parenthesis.
(1 point)
Linear Function
has the greater rate of change.
Linear Function 2 has the greater rate of change.
Use the table to answer the question. in as many scentices as you can
Day of the Week Number of Children in the Car
Sunday 2
Monday 4
Tuesday 4
Wednesday 3
Thursday 4
Friday 3
Saturday 0
Describe the meaning of the word function in math. Then consider the table. Why does this table show a function?
Day of the Week Number of Children in the Car
Sunday 2
Monday 4
Tuesday 4
Wednesday 3
Thursday 4
Friday 3
Saturday 0
Describe the meaning of the word function in math. Then consider the table. Why does this table show a function?
In mathematical terms, a function represents a relationship between two sets of variables, where each input (independent variable) corresponds to exactly one output (dependent variable). Essentially, a function pairs each element from the first set with exactly one element from the second set.
In the given table, the first set of variables represents different days of the week (independent variable) while the second set represents the number of children in the car (dependent variable). The table shows that for each specific day of the week, there is a unique corresponding number of children in the car. For example, on Sunday, there are 2 children in the car, and this pairing is consistent with no other day having 2 children. This one-to-one correspondence between the days of the week and the number of children in the car fulfills the criteria for a function. Therefore, this table represents a function because each day of the week is associated with a single, specific number of children in the car, demonstrating the fundamental concept of a function in mathematics.
In the given table, the first set of variables represents different days of the week (independent variable) while the second set represents the number of children in the car (dependent variable). The table shows that for each specific day of the week, there is a unique corresponding number of children in the car. For example, on Sunday, there are 2 children in the car, and this pairing is consistent with no other day having 2 children. This one-to-one correspondence between the days of the week and the number of children in the car fulfills the criteria for a function. Therefore, this table represents a function because each day of the week is associated with a single, specific number of children in the car, demonstrating the fundamental concept of a function in mathematics.
1 answer