Question

Example

Use a graph to determine whether the function is a linear function.
Input: x, a number; Output: y, 2 more than-1 times x
Make a table of input and output values.
Input (x)
Output (y)
-2 -1 0
1 2
4 3 2 1 0
Graph the (input, output) pairs. The points lie on a
straight line. Plotting more points will continue to
follow the same straight line. The function is linear.
-2
1
a. What is an equation that represents the rule in the Example?
У=муть
b. Use the equation to explain why the rule is a linear function.
O
-2
4

Answer 1

a. y = -x +2

b. x appears to the first power (only)

Explanation:

You want an equation and an explanation of why it is linear for the rule "input: x; output: y, 2 more than -1 times x".

a. Equation

The given wording tells you what the equation is:

y = 2 + (-1·x) . . . . . . 2 more than -1 times x

y = -x +2 . . . . . simplified

b. Linear

The equation is a linear equation because the variable x only shows up to the first power.