Question

give the slope and y-intercept of the line whose equation is given. then graph the linear function.
$f(x) = -dfrac{3}{4}x + 4$

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the slope is $-dfrac{3}{4}$.
(simplify your answer. type an integer or a fraction.)
b. the slope is undefined.

select the correct choice below and, if necessary, fill in the answer box to complete your choice.

a. the y-intercept is \boxed{}.
(simplify your answer. type an integer or a fraction.)
b. there is no y-intercept.

Explanation:

Step1: Recall the 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. In the function \(f(x)=-\frac{3}{4}x + 4\), we can think of \(y=f(x)\), so it is in the form \(y=mx + b\).

Step2: Identify the slope and \(y\) - intercept

For the equation \(y =-\frac{3}{4}x+4\), comparing with \(y = mx + b\):

• The coefficient of \(x\) is the slope \(m\). So, \(m =-\frac{3}{4}\), which we already saw from the first part of the problem.
• The constant term \(b\) is the \(y\) - intercept. Here, when \(x = 0\), \(y=b\). In the equation \(y=-\frac{3}{4}x + 4\), when \(x = 0\), \(y = 4\). So the \(y\) - intercept is \(4\).

Answer:

For the \(y\) - intercept:
The correct choice is A. The \(y\) - intercept is \(4\).