A functionf(x)

Question

is graphed on the coordinate plane.

What is the function rule in slope-intercept form?



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f(x)=


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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:

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