Question

choose the correct function/equation for the following description.
a linear function whose graph has y - intercept (0, 6)

choose the correct answer below.
a. $f(x)=6x + 1$
b. $f(x)=3x + 6$
c. $f(x)=x - 6$
d. $f(x)=-6x + 5$

Explanation:

Step1: Recall linear function form

The slope - intercept form of a linear function is $f(x)=mx + b$, where $m$ is the slope and $b$ is the $y$-intercept (the value of $y$ when $x = 0$). For the point $(0,6)$, when $x = 0$, $y=6$, so $b = 6$.

Step2: Analyze each option

• Option A: For $f(x)=6x + 1$, when $x = 0$, $f(0)=6(0)+1=1

eq6$. So this is not correct.

• Option B: For $f(x)=3x + 6$, when $x = 0$, $f(0)=3(0)+6 = 6$. This matches the $y$-intercept $(0,6)$.
• Option C: For $f(x)=x-6$, when $x = 0$, $f(0)=0 - 6=-6

eq6$. So this is not correct.

• Option D: For $f(x)=-6x + 5$, when $x = 0$, $f(0)=-6(0)+5 = 5

eq6$. So this is not correct.

Answer:

B. $f(x)=3x + 6$