Question

find the slope and the y-intercept.

(f(x) = -3x - 6)

the slope is .

the y-intercept is ((0, )).

Explanation:

Identify the given linear function

We are given the linear function:

$$f(x) = -3x - 6$$

This is a Linear Equations representation where \(f(x)\) represents the dependent variable \(y\).

Recall the slope-intercept form

The standard slope-intercept form of a linear equation is:

$$y = mx + b$$

where \(m\) represents the slope of the line, and \((0, b)\) represents the y-intercept.

Compare the equations to find the slope

By comparing \(f(x) = -3x - 6\) directly with \(y = mx + b\):

• The coefficient of \(x\) is \(m = -3\).

Therefore, the slope of the line is \(-3\).

Compare the equations to find the y-intercept

By comparing \(f(x) = -3x - 6\) directly with \(y = mx + b\):

• The constant term is \(b = -6\).

The y-intercept is the point where the graph crosses the y-axis, which occurs when \(x = 0\).
Substituting \(x = 0\) gives \(f(0) = -6\), so the y-intercept is \((0, -6)\).

Answer:

Find the slope and the y-intercept.
\(f(x) = -3x - 6\)

The slope is <blank>-3</blank>.
The y-intercept is (0, <blank>-6</blank>).