Question

The coordinates of three points in the plane are given below.
A= (-1, 2)
B=(4,2)
C=(-1, -3)
What is the equation of the line through b and c?

Answer 1

To find the equation of the line that passes through the points \( B = (4, 2) \) and \( C = (-1, -3) \), we will follow these steps:

1. **Calculate the slope (m)** of the line using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
where \( (x_1, y_1) = B = (4, 2) \) and \( (x_2, y_2) = C = (-1, -3) \).

Substituting in the coordinates of points B and C:
\[
m = \frac{-3 - 2}{-1 - 4} = \frac{-5}{-5} = 1
\]

2. **Use the point-slope form of the equation of a line**, which is:
\[
y - y_1 = m(x - x_1)
\]
We can use point \( B = (4, 2) \) for this, with \( m = 1 \):
\[
y - 2 = 1(x - 4)
\]
Simplifying this equation:
\[
y - 2 = x - 4
\]
\[
y = x - 2
\]

3. **Convert to slope-intercept form** if necessary, but here we already have:
\[
y = x - 2
\]

Thus, the equation of the line through points \( B \) and \( C \) is:
\[
\boxed{y = x - 2}
\]