The function f(x)

Question

is graphed on the coordinate plane.

What is f(−4)
?



Enter your answer in the box.

f(−4)
=

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 0 comma 2 end ordered pair and begin ordered pair 4 comma 0 end ordered pair.

Answer 1

To find \( f(-4) \) from the graph described, we first need to determine the equation of the line that passes through the points \( (0, 2) \) and \( (4, 0) \).

Let's find the slope \( m \) of the line using the slope formula:

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

Using the points \( (0, 2) \) and \( (4, 0) \):

\[ m = \frac{0 - 2}{4 - 0} = \frac{-2}{4} = -\frac{1}{2} \]

Now we have the slope. To find the equation of the line, we can use the point-slope form of the line equation:

\[ y - y_1 = m(x - x_1) \]

Using point \( (0, 2) \):

\[ y - 2 = -\frac{1}{2}(x - 0) \]

Simplifying gives:

\[ y - 2 = -\frac{1}{2}x \] \[ y = -\frac{1}{2}x + 2 \]

Now that we have the equation of the line \( f(x) = -\frac{1}{2}x + 2 \), we can find \( f(-4) \):

\[ f(-4) = -\frac{1}{2}(-4) + 2 \] \[ = 2 + 2 \] \[ = 4 \]

Thus, the value of \( f(-4) \) is:

\[ \boxed{4} \]