In the xy-plane, the graph of the linear function f has a slope of -3 and passes through t… — SAT

In the $xy$ -plane, the graph of the linear function $f$ has a slope of $-3$ and passes through the point $(4, 18)$ . What is the $y$ -coordinate of the $y$ -intercept of the graph of $f$ ?

Answer: 30

Answer

The correct answer is 30.

The equation of a linear function can be written in slope-intercept form as

f(x) = mx + b

, where

m

is the slope and

b

is the

y

-coordinate of the

y

-intercept. Substituting the given slope

m = -3

yields

f(x) = -3x + b

. Since the point

(4, 18)

lies on the graph of

f

, we substitute

x = 4

and

f(x) = 18

into the equation to get

18 = -3(4) + b

, which simplifies to

18 = -12 + b

. Adding

12

to both sides of the equation yields

b = 30

. Thus, the

y

-coordinate of the

y

-intercept of the graph of

f

30

Step-by-Step Solution

Write the general slope-intercept form of a linear equation.

f(x) = -3x + b

The slope of the line is given as

-3

, so we substitute

m = -3

into

f(x) = mx + b

Substitute the point

(4, 18)

into the equation.

18 = -3(4) + b

Since the graph of

f

passes through

(4, 18)

, these coordinates must satisfy the function equation.

Solve for the

y

-intercept

b

b = 30

Simplify to

18 = -12 + b

, and then add

12

to both sides to isolate

b

Key Concept

Finding the equation of a line using its slope and a point.

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