Question

write an equation of the line
(-2,-1) & (0,1)

Answer 1

To write the equation of the line that passes through the points \((-2, -1)\) and \((0, 1)\), we can use the two-point form of the line equation.

First, we need to find the slope (m) of the line using the formula:

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

Let \((x_1, y_1) = (-2, -1)\) and \((x_2, y_2) = (0, 1)\):

\[
m = \frac{1 - (-1)}{0 - (-2)} = \frac{1 + 1}{0 + 2} = \frac{2}{2} = 1
\]

Now that we have the slope \(m = 1\), we can use the point-slope form of the equation of the line, which is:

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

Using the point \((0, 1)\) (you can use either point), we have:

\[
y - 1 = 1(x - 0)
\]

This simplifies to:

\[
y - 1 = x
\]
\[
y = x + 1
\]

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

\[
\boxed{y = x + 1}
\]