Question

A line passes through the points (6,10) and (18,6). What is the equation of the line in slope-intercept form?
A: y= -1/3x +12
B: y= -3x +12
C: y=3x + 6

Answer 1

To find the equation of the line passing through the points (6,10) and (18,6), we first need to determine the slope (m) using the formula:

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

Substituting the coordinates of the two points, \((x_1, y_1) = (6, 10)\) and \((x_2, y_2) = (18, 6)\), we have:

\[
m = \frac{6 - 10}{18 - 6} = \frac{-4}{12} = -\frac{1}{3}
\]

Now that we have the slope, we can use the point-slope form of the equation of a line, which is:

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

Using one of the points, (6,10), we substitute \(m = -\frac{1}{3}\), \(x_1 = 6\), and \(y_1 = 10\):

\[
y - 10 = -\frac{1}{3}(x - 6)
\]

Now we distribute the slope on the right side:

\[
y - 10 = -\frac{1}{3}x + 2
\]

Next, we add 10 to both sides to solve for \(y\):

\[
y = -\frac{1}{3}x + 2 + 10
\]
\[
y = -\frac{1}{3}x + 12
\]

Thus, the equation of the line in slope-intercept form is:

\[
y = -\frac{1}{3}x + 12
\]

The correct answer is **A: y = -\frac{1}{3}x + 12**.