Question

A functionf(x)
is graphed on the coordinate plane.


What is the function rule in slope-intercept form?



Enter your answer in the box.

f(x)=


$\text{Basic}$
$x$$y$$x^2$$\sqrt{ }$$\frac{x}{ }$
$x\frac{ }{ }$
$x^{ }$$x_{ }$$\degree$$\left(\right)$$\abs{ }$$\pi$$\infty$
Graph of a line on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A line passes through the points begin ordered pair negative 2 comma 2 end ordered pair and begin ordered pair 4 comma negative 1 end ordered pair.

Answer 1

To find the function rule in slope-intercept form \( f(x) = mx + b \), we need to first determine the slope \( m \) and the y-intercept \( b \) from the given points.

The two points provided are \((-2, 2)\) and \((4, -1)\).

1. **Calculate the slope \( m \)**:

The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Substituting the coordinates of the points:

\[
m = \frac{-1 - 2}{4 - (-2)} = \frac{-3}{4 + 2} = \frac{-3}{6} = -\frac{1}{2}
\]

So, the slope \( m \) is \(-\frac{1}{2}\).

2. **Use the slope-intercept form to find \( b \)**:

We can use one of the points to solve for \( b \). Let's use the point \((-2, 2)\):

Using the slope-intercept equation \( y = mx + b \):

\[
2 = -\frac{1}{2}(-2) + b
\]

Calculating the right side:

\[
2 = 1 + b
\]

Now, solving for \( b \):

\[
b = 2 - 1 = 1
\]

3. **Write the complete function**:

Now that we have \( m = -\frac{1}{2} \) and \( b = 1 \), we can put it all together:

\[
f(x) = -\frac{1}{2}x + 1
\]

So, the function rule in slope-intercept form is:

\[
f(x) = -\frac{1}{2}x + 1
\]