Question - Converting Function to Slope-Intercept Form
Solution:
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).
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