Question

Determine the equation of the line that passes through the points (2, 5) and (8, 11) on a coordinate plane

Answer 1

To determine the equation of the line that passes through the points \((2, 5)\) and \((8, 11)\), we can follow these steps:

1. **Calculate the slope (m)** of the line using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Here, \((x_1, y_1) = (2, 5)\) and \((x_2, y_2) = (8, 11)\).

Substituting the values:
\[
m = \frac{11 - 5}{8 - 2} = \frac{6}{6} = 1
\]

2. **Use the point-slope form** of the equation of a line, which is given by:
\[
y - y_1 = m(x - x_1)
\]
We can use either of the points; we'll use \((2, 5)\).

Substituting in \(m = 1\), \(x_1 = 2\), and \(y_1 = 5\):
\[
y - 5 = 1(x - 2)
\]

3. **Simplify this equation**:
\[
y - 5 = x - 2
\]
\[
y = x - 2 + 5
\]
\[
y = x + 3
\]

Thus, the equation of the line in slope-intercept form is:
\[
\boxed{y = x + 3}
\]