The table below shows some values of the linear function f. | x | f(x) | | :--- | :--- | | 1 | 5 | | 4 | 17 | | 7 | 29 | What is the slope of the graph of f in the xy-plane?

The table below shows some values of the linear function f. | x | f(x) | | :--- | :--- | |… — SAT

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

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

The slope of the graph of

f

in the

xy

-plane is

4

The slope of a linear function can be found using any two points from the table,

(x_1, y_1)

and

(x_2, y_2)

, with the formula

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

. Using the points

(1, 5)

and

(4, 17)

, the slope is

\frac{17 - 5}{4 - 1} = 4

Select two points from the table to calculate the slope.

Using the points

(1, 5)

and

(4, 17)

, we have

x_1 = 1

y_1 = 5

x_2 = 4

, and

y_2 = 17

Any two points on a line can be used to find its constant slope.

Apply the slope formula

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

m = \frac{17 - 5}{4 - 1}

The slope formula calculates the ratio of the change in the vertical direction (

y

) to the change in the horizontal direction (

x

Simplify the expression to find the final slope value.

m = \frac{12}{3} = 4

Subtracting the coordinates and dividing gives the simplified slope.

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

Estimated Time:45s