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

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 $m = \frac{1}{4}$ 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.

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, $b = -10$.

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

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

Final Answer