Question

Which equation represents the line that passes through the points (5, 12) and (3, 8)?

A) ( y = 2x + 2 )
B) ( y = 2x + 4 )
C) ( y = 2x + 6 )
D) ( y = 2x + 8 )

Answer 1

To find the equation of the line that passes through the points (5, 12) and (3, 8), we first need to determine the slope (m) of the line using the formula:

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

Let (x₁, y₁) = (5, 12) and (x₂, y₂) = (3, 8). Calculating the slope:

\[
m = \frac{8 - 12}{3 - 5} = \frac{-4}{-2} = 2
\]

Now that we have the slope \(m = 2\), we can use point-slope form of the line equation, \(y - y_1 = m(x - x_1)\). We can use one of the points; let's use (5, 12):

\[
y - 12 = 2(x - 5)
\]

Distributing the 2:

\[
y - 12 = 2x - 10
\]

Now, solving for \(y\):

\[
y = 2x - 10 + 12
\]
\[
y = 2x + 2
\]

Thus, the equation of the line is:

\[
y = 2x + 2
\]

The correct answer is:

**A) \(y = 2x + 2\)**.