Question

the graph of a linear function f is shown to the right. (a) identify the slope, y-intercept, and x-intercept. (b) write the equation that defines f. a) the slope is $-\frac{1}{4}$ (type an integer or a simplified fraction ) the y-intercept is $(0, 3)$ (type an ordered pair type an integer or a simplified fraction ) the x-intercept is \\(\square\\) (type an ordered pair type an integer or a simplified fraction )

Explanation:

Step1: Recall the equation of a line

The equation of a line in slope - intercept form is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. We know that \(m=-\frac{1}{4}\) and \(b = 3\) (since the \(y\) - intercept is \((0,3)\)), so the equation of the line is \(y=-\frac{1}{4}x + 3\).

Step2: Find the \(x\) - intercept

The \(x\) - intercept is the point where \(y = 0\). Substitute \(y = 0\) into the equation \(y=-\frac{1}{4}x + 3\):
\[

$$\begin{align*} 0&=-\frac{1}{4}x+3\\ \frac{1}{4}x&=3\\ x&=3\times4\\ x& = 12 \end{align*}$$

\]
So the \(x\) - intercept is the point \((12,0)\) because when \(y = 0\), \(x = 12\).

Answer:

The \(x\) - intercept is \((12,0)\)