Which of the following is a linear function?
x2 = 5y
x = 3 + y2
x = 5 + y
x3 = 6y2
The linear function from the given options is x = 5 + y.
Which of the following is a linear function?
y = log(x3 + 9)
y = sin(2x)
y = e(x – 4)
y = 8
The linear function from the given options is y = 8.
The table given below shows the total amount saved by Tim every week.
Week
Money Saved ($)
1
15
2
20
3
25
4
30
5
35
Which of the following is true about the table of values?
Linear and Rate of change is $15
Non-linear function and Rate of change is $25
Linear function and Rate of change is $5
Non-linear function and Rate of change is $3
To determine if the table represents a linear or non-linear function, we need to check if there is a constant rate of change.
The rate of change is calculated by dividing the change in the dependent variable (money saved) by the change in the independent variable (week).
Looking at the table, we can see that for every increase of 1 week, there is an increase of $5 in the money saved. This means that the rate of change is $5 per week.
Since there is a constant rate of change, the table represents a linear function. Therefore, the option that is true about the table of values is:
Linear function and Rate of change is $5
A linear function is a function whose graph is a straight line. Let's analyze each of the given equations to determine if it represents a linear function.
1. x^2 = 5y: This equation is not linear because it contains a squared term (x^2).
2. x = 3 + y^2: This equation is not linear because it contains a squared term (y^2).
3. x = 5 + y: This equation is linear because both x and y appear as separate terms without any squared terms or other non-linear operations.
4. x^3 = 6y^2: This equation is not linear because it contains a cubed term (x^3) and a squared term (y^2).
So, the linear function among the given options is:
x = 5 + y.
To determine which of the given equations is a linear function, we need to examine the general form of a linear function.
A linear function is usually represented by the equation y = mx + b, where m is the slope and b is the y-intercept.
Let's analyze each equation and check if it fits the criteria of a linear function:
1. x^2 = 5y:
This equation is not in the standard form of a linear function since it contains an exponent on the x variable. Therefore, it is not a linear function.
2. x = 3 + y^2:
Similarly to the previous equation, this equation also contains an exponent on the y variable, making it non-linear.
3. x = 5 + y:
In this equation, x is equal to a constant value plus y. This equation is in the standard form of a linear function since it can be rearranged to y = x - 5. Thus, it represents a linear function.
4. x^3 = 6y^2:
Similar to the first and second equations, this equation contains exponents on both x and y variables. Hence, it is not a linear function.
In conclusion, the only equation that represents a linear function among the given options is x = 5 + y.