Question

Write the function for the graph (1,8) (0,4)

Answer 1

To find the equation of the line that passes through the two points \((1, 8)\) and \((0, 4)\), we first need to calculate the slope (m) of the line.

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

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

Using the points \((0, 4)\) (let's designate this as \((x_1, y_1)\)) and \((1, 8)\) (designated as \((x_2, y_2)\)):

\[
m = \frac{8 - 4}{1 - 0} = \frac{4}{1} = 4
\]

Now, we have the slope \( m = 4 \). With the slope and one of the points, we can use the point-slope form of the equation of a line:

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

Using point \((0, 4)\):

\[
y - 4 = 4(x - 0)
\]

Simplifying this gives us:

\[
y - 4 = 4x
\]

\[
y = 4x + 4
\]

Thus, the function for the graph that includes the points \((1, 8)\) and \((0, 4)\) is:

\[
y = 4x + 4
\]