The table below shows some values of the linear function g. | x | g(x) | |---|---| | 2 | 5 | | 4 | 11 | | 6 | 17 | What is the slope of the graph of g in the xy-plane?

The table below shows some values of the linear function g. | x | g(x) | |---|---| | 2 | 5… — SAT

The table below shows some values of the linear function $g$ .

$x$	$g(x)$
$2$	$5$
$4$	$11$
$6$	$17$

What is the slope of the graph of $g$ in the $xy$ -plane?

A
$\frac{1}{3}$
B
$6$
$3$ Answer
D
$\frac{5}{2}$

Answer

The slope of the graph is

3

The slope of a linear function is the constant rate of change, calculated as the change in the function values divided by the change in the input values. Choosing the points

(2, 5)

and

(4, 11)

, the slope is

\frac{11 - 5}{4 - 2} = \frac{6}{2} = 3

. This same slope is obtained using any other pair of points from the table, such as

(4, 11)

and

(6, 17)

, where the slope is

\frac{17 - 11}{6 - 4} = \frac{6}{2} = 3

Step-by-Step Solution

Select two points from the table to find the change in the input and output values.

Using the points

(2, 5)

and

(4, 11)

, the change in the output

g(x)

11 - 5 = 6

, and the change in the input

x

4 - 2 = 2

The slope is defined as the change in the vertical coordinate divided by the change in the horizontal coordinate.

Divide the change in

g(x)

by the change in

x

to find the slope.

The slope is

\frac{6}{2} = 3

Dividing the vertical change by the horizontal change yields the constant rate of change of the linear function.

Key Concept

Finding the slope of a linear function from a table of values

Estimated Time:45s

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