Question

a function is shown.
$f(x) = -\frac{7}{8}x + 11$
complete the statements.
the function’s $x$-intercept occurs at
the function’s $y$-intercept occurs at
options: $(-7, 0)$, $left(-\frac{7}{8}, 0
ight)$, $(8, 0)$, $(11, 0)$, $left(\frac{88}{7}, 0
ight)$, $(0, -7)$, $left(0, -\frac{7}{8}
ight)$, $(0, 8)$, $(0, 11)$, $left(0, \frac{88}{7}
ight)$

Explanation:

Step1: Find x - intercept

To find the x - intercept, we set \(y = f(x)=0\) in the function \(f(x)=-\frac{7}{8}x + 11\).
So, \(0=-\frac{7}{8}x + 11\).
Add \(\frac{7}{8}x\) to both sides: \(\frac{7}{8}x=11\).
Multiply both sides by \(\frac{8}{7}\): \(x = 11\times\frac{8}{7}=\frac{88}{7}\).
So the x - intercept is at \((\frac{88}{7},0)\).

Step2: Find y - intercept

To find the y - intercept, we set \(x = 0\) in the function \(f(x)=-\frac{7}{8}x + 11\).
Substitute \(x = 0\) into the function: \(f(0)=-\frac{7}{8}(0)+11=11\).
So the y - intercept is at \((0,11)\).

Answer:

The function's x - intercept occurs at \(\boldsymbol{(\frac{88}{7},0)}\)
The function's y - intercept occurs at \(\boldsymbol{(0,11)}\)