Questions: Question 10
5 pts
Write a formula for a linear function f whose graph satisfies the conditions.
Slope: 1/3 ; y-intercept: 4
f(x)=1/3 x+4
f(x)=1/3 x-4
f(x)=-1/3 x-4
f(x)=-1/3 x+4
Transcript text: Question 10
5 pts
Write a formula for a linear function $f$ whose graph satisfies the condítions.
Slope: $\frac{1}{3} ; y$-intercept: 4
$f(x)=\frac{1}{3} x+4$
$f(x)=\frac{1}{3} x-4$
$f(x)=-\frac{1}{3} x-4$
$f(x)=-\frac{1}{3} x+4$
Solution
Solution Steps
To find the correct formula for the linear function, we need to use the slope-intercept form of a linear equation, which is \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Given the slope \(\frac{1}{3}\) and y-intercept 4, we can directly substitute these values into the formula.
Step 1: Identify the Linear Function
The linear function is expressed in the slope-intercept form \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Given the slope \( m = \frac{1}{3} \) and the y-intercept \( b = 4 \), we can write the function as:
\[
f(x) = \frac{1}{3}x + 4
\]
Step 2: Evaluate the Function at \( x = 0 \)
To find the value of the function at \( x = 0 \):
\[
f(0) = \frac{1}{3}(0) + 4 = 4
\]
Step 3: Conclusion
The output of the function when \( x = 0 \) is \( 4 \). This confirms that the y-intercept is indeed \( 4 \).
Final Answer
The correct formula for the linear function is:
\[
\boxed{f(x) = \frac{1}{3}x + 4}
\]