1. Identify the following functions as linear or nonlinear:
xy = -9
y = 3x
x + 7 = y
y = x - 4
y = x^2
x + y - 20 = 2x
1/2x = y
y = 5/x
y = 30 - x^2
thank you
Ms. Sue can you help
L --- linear
N --- non-linear
xy = -9 --- N
y = 3x --- L
x + 7 = y --- L
y = x - 4 --- L
y = x^2 --- N
x + y - 20 = 2x --- L
1/2x = y ---- L
y = 5/x ---- N
y = 30 - x^2 ---- N
Did you notice why some are L and some are N ?
To determine whether a function is linear or nonlinear, we need to examine the form of the equation and check if it satisfies the properties of a linear function.
1. xy = -9: This is a nonlinear function because it contains terms with both x and y multiplied together.
2. y = 3x: This is a linear function because it has a constant rate of change and does not involve any higher powers or products of variables.
3. x + 7 = y: This is a linear function because it can be rearranged to the standard form y = mx + b, where m (the coefficient of x) is 1, and b (the y-intercept) is 7.
4. y = x - 4: This is a linear function because it can also be rearranged to the standard form y = mx + b, where m = 1 and b = -4.
5. y = x^2: This is a nonlinear function because it contains the squared term of x.
6. x + y - 20 = 2x: This is a linear function because it can be simplified and rearranged to y = -x + 20, which is in the standard form of a linear equation.
7. 1/2x = y: This is a linear function because it can be rewritten as y = (1/2)x, which is in the standard form.
8. y = 5/x: This is a nonlinear function because it involves the reciprocal of x, resulting in a curve when graphed.
9. y = 30 - x^2: This is a nonlinear function because it contains the squared term of x.