Questions: Find the linear function with the following properties. f(0)=-10 Slope of f=1/4

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. \[ \begin{array}{c} f(0)=-10 \\ \text { Slope of } \mathrm{f}=\frac{1}{4} \end{array} \]
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Solution

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Solution Steps

To find the linear function, we need to use the point-slope form of a linear equation, which is y=mx+b y = mx + b , where m m is the slope and b b is the y-intercept. We are given the slope m=14 m = \frac{1}{4} and the function value at x=0 x = 0 , which is the y-intercept b=10 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 m = 0.25 , and the function value at x=0 x = 0 , which is f(0)=10 f(0) = -10 . This value at x=0 x = 0 represents the y-intercept, b=10 b = -10 .

Step 2: Use the Point-Slope Form

The general form of a linear function is given by: f(x)=mx+b f(x) = mx + b Substituting the given values, we have: f(x)=0.25x10 f(x) = 0.25x - 10

Step 3: Verify the Function

To ensure the function is correct, substitute x=0 x = 0 into the equation: f(0)=0.25×010=10 f(0) = 0.25 \times 0 - 10 = -10 This confirms that the function satisfies the given condition f(0)=10 f(0) = -10 .

Final Answer

f(x)=14x10 \boxed{f(x) = \frac{1}{4}x - 10}

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