For the linear function f, the graph of y = f(x) has a slope of 3 and contains the point (… — SAT

For the linear function $f$ , the graph of $y = f(x)$ has a slope of $3$ and contains the point $(2, 7)$ . The graph of another linear function, $g$ , is parallel to the graph of $f$ . If $g(0) = -4$ , what is the value of $g(5)$ ?

Answer: 11

Answer

Since the graph of

g

is parallel to the graph of

f

, it has the same slope of

3

. The value

g(0) = -4

indicates that the

y

-intercept of the graph of

g

-4

. Thus, the equation for

g(x)

g(x) = 3x - 4

. Evaluating this function at

x = 5

gives

g(5) = 3(5) - 4 = 11

Step-by-Step Solution

Determine the slope of the function

g

The slope of

g

3

Parallel lines in the coordinate plane have equal slopes, and the slope of the graph of

f

is given as

3

Write the equation for

g(x)

g(x) = 3x - 4

Using the slope-intercept form

g(x) = mx + b

with slope

m = 3

and

y

-intercept

b = g(0) = -4

Evaluate

g(5)

11

Substitute

x = 5

into the equation for

g(x)

to get

g(5) = 3(5) - 4 = 11

Key Concept

Parallel lines have the same slope. A linear function can be written in slope-intercept form,

y = mx + b

, where

m

is the slope and

b

is the

y

-intercept.

Question

Answer

Step-by-Step Solution

Key Concept

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