Question

the function f is defined by $f(x) = \frac{7}{13}x$. what is the slope of the graph of $y = f(x)$ in the xy - plane?
a 0
b $\frac{7}{13}$
c $\frac{13}{7}$
d the slope is undefined.

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.

Step2: Analyze the given function

The function is given as \(f(x)=\frac{7}{13}x\). We can rewrite \(y = f(x)\), so the equation of the line is \(y=\frac{7}{13}x+0\). Comparing this with the slope - intercept form \(y = mx + b\), we can see that \(m=\frac{7}{13}\) (the coefficient of \(x\)) and \(b = 0\).

Answer:

B. \(\frac{7}{13}\)