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