Questions: Find the linear function with the following properties.
f(0)=-10
Slope of f=1/4
Transcript text: Find the linear function with the following properties.
\[
\begin{array}{c}
f(0)=-10 \\
\text { Slope of } \mathrm{f}=\frac{1}{4}
\end{array}
\]
Solution
Solution Steps
To find the linear function, we need to use the point-slope form of a linear equation, which is y=mx+b, where m is the slope and b is the y-intercept. We are given the slope m=41 and the function value at x=0, which is the y-intercept b=−10. Substitute these values into the equation to find the linear function.
Step 1: Identify the Given Information
We are given the slope of the linear function, m=0.25, and the function value at x=0, which is f(0)=−10. This value at x=0 represents the y-intercept, b=−10.
Step 2: Use the Point-Slope Form
The general form of a linear function is given by:
f(x)=mx+b
Substituting the given values, we have:
f(x)=0.25x−10
Step 3: Verify the Function
To ensure the function is correct, substitute x=0 into the equation:
f(0)=0.25×0−10=−10
This confirms that the function satisfies the given condition f(0)=−10.