Example Question - converting function

Converting Function to Slope-Intercept Form

The function given in the image is: \[ f(x) = -2 \left( x + \frac{1}{4} \right) - \frac{49}{8} \] To express the function in the form of y-intercept, we need to simplify it while keeping it in the form of \( y = mx + b \), where \( m \) stands for the slope and \( b \) is the y-intercept. Let's simplify the function: \[ f(x) = -2x - \frac{1}{2} - \frac{49}{8} \] To combine the constant terms, we need a common denominator. The common denominator for \( \frac{1}{2} \) and \( \frac{49}{8} \) is 8. So let's convert \( \frac{1}{2} \) to have the denominator of 8: \[ - \frac{1}{2} = - \frac{4}{8} \] Now rewritting the equation we have: \[ f(x) = -2x - \frac{4}{8} - \frac{49}{8} = -2x - \frac{53}{8} \] So the function in the form of intercept is: \[ f(x) = -2x - \frac{53}{8} \] This function is now in slope-intercept form with \( m = -2 \) (the slope) and \( b = -\frac{53}{8} \) (the y-intercept).