The table below shows several values of x and their corresponding values of f(x) for the linear function f. | x | f(x) | | :---: | :---: | | 2 | 7 | | 5 | 13 | | 8 | 19 | What is the slope of the graph of y = f(x) in the xy-plane?

The table below shows several values of x and their corresponding values of f(x) for the l… — SAT

The table below shows several values of $x$ and their corresponding values of $f(x)$ for the linear function $f$ .

$x$	$f(x)$
$2$	$7$
$5$	$13$
$8$	$19$

What is the slope of the graph of $y = f(x)$ in the $xy$ -plane?

2Answer
B
0.5
C
3
D
4

Answer

The slope of the graph of

y = f(x)

is 2.

The slope of a linear function represents the constant rate of change of the function values with respect to the input values. Using any two points from the table, such as

(2, 7)

and

(5, 13)

, the slope

m

can be calculated using the slope formula:

m = \frac{f(x_2) - f(x_1)}{x_2 - x_1} = \frac{13 - 7}{5 - 2} = \frac{6}{3} = 2

. Therefore, the slope of the graph of

y = f(x)

2

Step-by-Step Solution

Select two points from the given table.

Two points are

(2, 7)

and

(5, 13)

To find the slope of a linear function, we need to calculate the rate of change between any two points on the line.

Apply the slope formula

m = \frac{y_2 - y_1}{x_2 - x_1}

m = \frac{13 - 7}{5 - 2} = \frac{6}{3} = 2

Calculating the ratio of the vertical change (change in

f(x)

) to the horizontal change (change in

x

) yields the constant slope of the linear function.

Key Concept

Calculating the slope of a linear function from a table of values.

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