Question

Complete the equation of the line through
\[(2,1)\] and
\[(5,-8)\].
Use exact numbers.
\[y=\]

Answer 1

To find the equation of the line through the points \((2, 1)\) and \((5, -8)\), we first need to determine 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:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Assigning the points \((x_1, y_1) = (2, 1)\) and \((x_2, y_2) = (5, -8)\), we substitute these values into the formula:
\[
m = \frac{-8 - 1}{5 - 2} = \frac{-9}{3} = -3
\]

Now that we have the slope, we can use the point-slope form of a linear equation. The point-slope form is expressed as:
\[
y - y_1 = m(x - x_1)
\]

Using the point \((2, 1)\) and the slope \(m = -3\):
\[
y - 1 = -3(x - 2)
\]

Next, we will simplify this equation:
\[
y - 1 = -3x + 6
\]
\[
y = -3x + 7
\]

Therefore, the equation of the line is:
\[
\boxed{y = -3x + 7}
\]