Linear Function

Question

The graph and the table each represent a different linear function. When x =6, which of the two
functions has the greater y-value?

The coordinates on the x axis are (3,0)
The coordinates on the y axis are (0, -3)

The table is as follows
X Values : -2 -1 0 1 2
Y Values : -2 0 2 4 6

[A]The function represented in the graph has the greater y-value when x =6.
[B] The function represented in the table has the greater y-value when x =6.
[C] The two functions have the same y-value when x =6.

Answer 1

Find the slope between the two points on the graph.

 

slope = (-3 - 0) / (0 - 3)

        = -3 / -3

        = 1

 

The line for this one is

 

f(x) = x - 3

 

 

In the table, there is a common difference among x and y values.  The common difference among x is 1.  The common difference among y is 2.  Therefore, you slope is

 

slope = 2

 

Using the y-intercept (0, 2), we get the line

 

g(x) = 2x + 2

 

 

Evaluate f(6) and g(6).  Which has the greater value?