Question

Write the equation in point slope form of line passing through the points -2, 1/2 and two, 3/2

Answer 1

To write the equation of a line in point-slope form, we first need to find the slope of the line that passes through the given points \((-2, \frac{1}{2})\) and \( (2, \frac{3}{2})\).

The slope \(m\) can be calculated using the formula:

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

Where:
- \((x_1, y_1) = (-2, \frac{1}{2})\)
- \((x_2, y_2) = (2, \frac{3}{2})\)

Substituting the values in:

\[
m = \frac{\frac{3}{2} - \frac{1}{2}}{2 - (-2)} = \frac{\frac{3}{2} - \frac{1}{2}}{2 + 2} = \frac{\frac{2}{2}}{4} = \frac{1}{4}
\]

Now that we have the slope \(m = \frac{1}{4}\), we can use one of the points to write the equation in point-slope form. Let's use the point \((-2, \frac{1}{2})\).

The point-slope form of a line is given by:

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

Substituting in \(m\), \(x_1\), and \(y_1\):

\[
y - \frac{1}{2} = \frac{1}{4}(x - (-2))
\]

This simplifies to:

\[
y - \frac{1}{2} = \frac{1}{4}(x + 2)
\]

So, the equation of the line in point-slope form is:

\[
y - \frac{1}{2} = \frac{1}{4}(x + 2)
\]