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

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 $f(x)=\frac{1}{3} x+4$ $f(x)=\frac{1}{3} x-4$ $f(x)=-\frac{1}{3} x-4$ $f(x)=-\frac{1}{3} x+4$
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Solution

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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: \[ \boxed{f(x) = \frac{1}{3}x + 4} \]

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