The linear functions are:
y = 6x - 2
x + y = 12
y = x
The non-linear functions are:
y = 3x³ + 5
y = x² - 33
Explanation:
Linear functions can be written in the form y = mx+b, where m is the slope and b is the y-intercept. In linear functions, the x variable has at highest an exponent of 1.
The first equation, y = 6x - 2, is in slope-intercept form; it is linear.
The second equation, y = 3x³ + 5, has an x with an exponent greater than 1; it is non-linear.
The third equation, y = x² - 33, has an x with an exponent greater than 1; it is non-linear.
The fourth equation, x + y = 12, can be written as y=mx+b:
x+y=12
Subtract x from both sides:
x+y-x=12-x
y = -x+12
This is a <span><u><em>linear </em></u></span>function.
The <u>fifth </u>equation, y = x, is in the form y=mx+b; in this case, m=1 and b=0. This is <u><em>linear</em></u>.
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Remember that the y-intercept is where the function has a value of 
and the x-intercept is where the function has a value of 
. Thus, to find the x-intercept and y-intercept, we can substitute these values into the equation and solve for the other variable.
<u>x-intercept</u>
Since the x-intecept has a y-value of 0, we can substitute this into the function and solve for 
.
The x-value of the x-intercept is 
and the y-value is 0, meaning that the x-intercept has coordinates 
.
<u>y-intercept</u>
Since the y-intercept has a x-value of 0, we can substitute this into the equation and solve for 
:
The y-value of the y-intercept is -3, meaning that the y-intercept of the function is 
.
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