Question

Which of the following is a point-slope equation of a line that passes through

Answer 1

Please, check the options of the question. The point-slope equation needs the slope, m, in the equation.

Answer:

The point-slope equation of the points (5,2) and (-1,-6) is

$\\ y - 2 = \frac{4}{3}(x-5)$  or,

$\\ y + 6 = \frac{4}{3}(x+1)$

which are the same as

$\\ 3y-4x+14 = 0$ , (which is not a point-slope equation, though)

Step-by-step explanation:

The point-slope equation is given by:

$\\ y - y_{1} = m(x - x_{1})$

Where m is the slope of the line:

$\\ m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Having the points (5,2) and (-1,-6), then

$\\ m = \frac{-6 - 2}{-1 -5}$

$\\ m = \frac{-8}{-6}$

$\\ m = \frac{4}{3}$

Then, the point-slope equation of the points (5,2) and (-1,-6) is

$\\ y - 2 = \frac{4}{3}(x-5)$ or

$\\ y + 6 = \frac{4}{3}(x+1)$

The below graph represents both lines (they are the same line).