Question

Complete the point-slope equation of the line through
\[(1,3)\] and
\[(5,1)\].
Use exact numbers.
\[y-3=\]

Answer 1

To find the point-slope equation of the line through the points \((1,3)\) and \((5,1)\), we first need to calculate the slope of the line using the formula:

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

Here, \((x_1, y_1) = (1, 3)\) and \((x_2, y_2) = (5, 1)\). Plugging in the values:

\[
m = \frac{1 - 3}{5 - 1} = \frac{-2}{4} = -\frac{1}{2}
\]

Now that we have the slope \(m = -\frac{1}{2}\), we can substitute this and the coordinates of one of the points into the point-slope equation:

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

Using the point \((1, 3)\):

\[
y - 3 = -\frac{1}{2}(x - 1)
\]

Thus, the completed point-slope equation is:

\[
y - 3 = -\frac{1}{2}(x - 1)
\]