Question

A line passes through the points (
–
2,4) and (2,
–
6). Which of the following is an equation of the line?

Answer 1

To determine the equation of the line that passes through the points \((-2, 4)\) and \((2, -6)\), we first need to calculate the slope of the line using the formula:

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

Here, \((x_1, y_1) = (-2, 4)\) and \((x_2, y_2) = (2, -6)\).

Plugging in the values, we have:

\[
m = \frac{-6 - 4}{2 - (-2)} = \frac{-10}{2 + 2} = \frac{-10}{4} = -\frac{5}{2}
\]

Now that we have the slope \( m = -\frac{5}{2} \), we can use the point-slope form of the line equation, which is given by:

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

We can use the point \((-2, 4)\) to write the equation:

\[
y - 4 = -\frac{5}{2}(x + 2)
\]

Distributing the slope on the right side:

\[
y - 4 = -\frac{5}{2}x - \frac{5}{2} \cdot 2
\]

\[
y - 4 = -\frac{5}{2}x - 5
\]

Now, add 4 to both sides to isolate \(y\):

\[
y = -\frac{5}{2}x - 5 + 4
\]

\[
y = -\frac{5}{2}x - 1
\]

So, the equation of the line is:

\[
y = -\frac{5}{2}x - 1
\]

This is the equation of the line that passes through the points \((-2, 4)\) and \((2, -6)\).