Question

Write the equation of the line passing through the points left parenthesis 44 comma 6 right parenthesis(44,6) and left parenthesis negative 4 comma negative 6 right parenthesis .(−4,−6).

Answer 1

To find the equation of the line passing through the points \((44, 6)\) and \((-4, -6)\), we can start by calculating the slope \(m\) of the line using the formula:

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

Let \((x_1, y_1) = (44, 6)\) and \((x_2, y_2) = (-4, -6)\). Substituting these values into the slope formula gives:

\[
m = \frac{-6 - 6}{-4 - 44} = \frac{-12}{-48} = \frac{1}{4}
\]

Now that we have the slope, we can use point-slope form to write the equation of the line. The point-slope form is given by:

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

Using point \((44, 6)\) and the slope \(m = \frac{1}{4}\):

\[
y - 6 = \frac{1}{4}(x - 44)
\]

Now we can simplify this equation:

\[
y - 6 = \frac{1}{4}x - \frac{44}{4}
\]

\[
y - 6 = \frac{1}{4}x - 11
\]

Adding \(6\) to both sides:

\[
y = \frac{1}{4}x - 11 + 6
\]

\[
y = \frac{1}{4}x - 5
\]

Thus, the equation of the line passing through the points \((44, 6)\) and \((-4, -6)\) is:

\[
y = \frac{1}{4}x - 5
\]