Question

What is the equation in point-slope form of a line that passes through the points (7, −8) and (−4, 6) ?


A. y + 6 = - 2/3 (x - 4)
B. y + 6 = - 14/11 (x - 4)
C. y - 6 = - 14/11 (x + 4)
D. y - 6 = - 2/3 (x + 4)

Answer 1

To find the equation in point-slope form of the line that passes through the points (7, −8) and (−4, 6), we first need to calculate the slope \( m \) of the line using the slope formula:

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

Using the points (7, −8) and (−4, 6):
- \( (x_1, y_1) = (7, -8) \)
- \( (x_2, y_2) = (-4, 6) \)

Substituting these values into the slope formula:

\[
m = \frac{6 - (-8)}{-4 - 7} = \frac{6 + 8}{-4 - 7} = \frac{14}{-11} = -\frac{14}{11}
\]

Now that we have the slope \( m = -\frac{14}{11} \), we can use the point-slope form of the equation of a line, which is:

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

We can use either of the two points, but let’s use (7, -8):

\[
y - (-8) = -\frac{14}{11}(x - 7)
\]

This simplifies to:

\[
y + 8 = -\frac{14}{11}(x - 7)
\]

Now we'll manipulate this to match one of the given answer choices. Let's convert it to a form that might fit the options more closely. We can express it based on the other point (-4, 6):

Using the second point (-4, 6), we write:

\[
y - 6 = -\frac{14}{11}(x + 4)
\]

Now we compare this with the options given:

C. \( y - 6 = -\frac{14}{11}(x + 4) \)

This option matches our equation, meaning the correct answer is:

**C.** \( y - 6 = -\frac{14}{11}(x + 4) \)