What is the equation of the line that passes through the points (-2, 3) and (2, 7)?

Solution:

Given, the line passes through the points (-2, 3) and (2, 7).

We have to find the equation of the line.

The equation of the line passing through two points is given by

\(\frac{y-y_{1}}{y_{2}-y_{1}}=\frac{x-x_{1}}{x_{2}-x_{1}}\)

So, \(\frac{y-3}{7-3}=\frac{x-(-2))}{2-(-2)}\)

\(\frac{y-3}{4}=\frac{x+2}{2+2}\)

\(\frac{y-3}{4}=\frac{x+2}{4}\)

Now, y-3 = x+2

On rearranging,

x - y + 3 + 2 = 0

x - y + 5 = 0

Therefore, the equation of the line is x - y + 5 = 0.

What is the equation of the line that passes through the points (-2, 3) and (2, 7)?

Summary:

The equation of the line that passes through the points (-2, 3) and (2, 7) is x - y + 5 = 0.