Question

Complete the point-slope equation of the line through (3,6)(3,6) and (5,-8)(5,−8). Use exact numbers.

Options:
A) y = -7x + 27y=−7x+27
B) y = -7x - 15y=−7x−15
C) y = -7x + 21y=−7x+21
D) y = -7x - 21y=−7x−21

Answer 1

The point-slope equation of the line through (3,6) and (5,-8) is y = -7x + 27.

Step-by-step explanation:

To find the point-slope equation of the line, we need to first calculate the slope using the formula:

slope = (change in y) / (change in x)

slope = (-8 - 6) / (5 - 3) = -14 / 2 = -7

Now that we have the slope, we can use the point-slope form of the equation:

y - y1 = m(x - x1)

Using the point (3, 6), we get:

y - 6 = -7(x - 3)

Expanding the equation gives us:

y - 6 = -7x + 21

Finally, rearranging the equation gives us:

y = -7x + 27