Question

through: (-2,5) and (0,-5)

Answer 1

To find the equation of the line that passes through the points \((-2, 5)\) and \((0, -5)\), we first need to calculate the slope of the line, given by the formula:

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

Using the points \((-2, 5)\) (let's call this \((x_1, y_1)\)) and \((0, -5)\) (let's call this \((x_2, y_2)\)), we have:

\[
m = \frac{-5 - 5}{0 - (-2)} = \frac{-10}{0 + 2} = \frac{-10}{2} = -5
\]

Now that we have the slope \(m = -5\), we can use the point-slope form of the equation of a line, which is:

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

Using the point \((0, -5)\):

\[
y - (-5) = -5(x - 0)
\]
\[
y + 5 = -5x
\]
\[
y = -5x - 5
\]

Thus, the equation of the line in slope-intercept form is:

\[
y = -5x - 5
\]

If we want to express the equation in standard form \(Ax + By = C\), we can rearrange it:

\[
5x + y = -5
\]

So, the equation of the line that passes through the points \((-2, 5)\) and \((0, -5)\) can be written in standard form as:

\[
5x + y = -5
\]