The table below shows some values of the linear function f. | x | f(x) | | :---: | :---: | | 2 | 11 | | 4 | 17 | | 6 | 23 | What is the y-coordinate of the y-intercept of the graph of y = f(x) 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 $y$ -coordinate of the $y$ -intercept of the graph of $y = f(x)$ in the $xy$ -plane?

Cevap: 5

The correct answer is 5, representing the y-coordinate of the y-intercept of the graph of f.

To find the

y

-intercept of the linear function, we first determine its slope using the points

(2, 11)

and

(4, 17)

from the table. The slope

m

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

. Next, we use the slope-intercept equation

f(x) = mx + b

. Substituting

m = 3

and the point

(2, 11)

gives

11 = 3(2) + b

, which simplifies to

11 = 6 + b

. Solving for

b

yields

5

. Therefore, the

y

-coordinate of the

y

-intercept of the graph of

f

5

Calculate the slope (

m

) of the linear function using two coordinate pairs from the table.

The slope is

m = 3

A linear function has a constant slope, which can be found using the formula

m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}

Substitute the slope and one of the points into the slope-intercept equation

f(x) = mx + b

to solve for the

y

-intercept

b

The

y

-intercept

b

5

The

y

-coordinate of the

y

-intercept of the graph of

y = f(x)

is the value of

b

in the equation

f(x) = mx + b

Finding the y-intercept of a linear function from a table of values.

Tahmini Süre:45s