For the linear function f, the value of f(0) is 3 and the value of f(5) is 18. What is the… — SAT

For the linear function $f$ , the value of $f(0)$ is $3$ and the value of $f(5)$ is $18$ . What is the slope of the graph of $y = f(x)$ in the $xy$ -plane?

Answer: 3

Answer

The slope of the graph of

y = f(x)

3

The slope of a linear function can be determined using any two points

(x_1, y_1)

and

(x_2, y_2)

on its graph with the formula

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

. The given function values

f(0) = 3

and

f(5) = 18

correspond to the coordinate points

(0, 3)

and

(5, 18)

respectively. Substituting these coordinates into the formula gives

m = \frac{18 - 3}{5 - 0} = \frac{15}{5} = 3

Step-by-Step Solution

Identify the coordinates of two points on the line using the given function values.

The function values

f(0) = 3

and

f(5) = 18

correspond to the points

(0, 3)

and

(5, 18)

on the graph of the function.

In function notation,

f(x) = y

represents a point

(x, y)

on the graph of the function.

Calculate the slope using the slope formula.

The slope

m

is calculated as

\frac{18 - 3}{5 - 0} = 3

The slope of a line is defined as the change in

y

divided by the change in

x

between any two points on the line.

Key Concept

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

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