Question

Which equation represents the line that passes through (–6, 7) and (–3, 6)?

y = –y equals negative StartFraction one-third EndFraction x plus 5.x + 9
y = –y equals negative StartFraction one-third EndFraction x plus 5.x + 5
y = –3x – 11y
y = –3x + 25

Answer 1

To find the equation of the line that passes through the points \((-6, 7)\) and \((-3, 6)\), we first need to determine the slope (m) of the line using the formula:

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

Here, \((x_1, y_1) = (-6, 7)\) and \((x_2, y_2) = (-3, 6)\):

\[
m = \frac{6 - 7}{-3 + 6} = \frac{-1}{3} = -\frac{1}{3}
\]

Now we can use the point-slope form of the line equation:

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

Substituting one of the points, say \((-6, 7)\), and the slope \(-\frac{1}{3}\):

\[
y - 7 = -\frac{1}{3}(x + 6)
\]

Now, let's rearrange this into slope-intercept form (y = mx + b):

\[
y - 7 = -\frac{1}{3}x - 2
\]
\[
y = -\frac{1}{3}x + 5
\]

Now, looking at your options, the equivalent equation is:

\[
y = -\frac{1}{3}x + 5
\]

Therefore, the correct answer is:

**y = –y equals negative StartFraction one-third EndFraction x plus 5.**