Question

Complete the point-slope equation of the line through (3,6)(3,6)left parenthesis, 3, comma, 6, right parenthesis and (5,-8)(5,−8)left parenthesis, 5, comma, minus, 8, right parenthesis.

Answer 1

Answer:

The required equation of line in point-slope form is:

$y-6 = -7(x-3)$

Step-by-step explanation:

Given points are:

(x1,y1) = (3,6)

(x2,y2) = (5,-8)

The point-slope form of an equation is given by:

$y-y_1 = m(x-x_1)$

Here m is slope of the line and (x1,y1) is a point on line

The slope is calculated using the formula:

$m = \frac{y_2-y_1}{x_2-x_1}$

Putting the values we get

$m = \frac{-8-6}{5-3}\\m=\frac{-14}{2}\\m= -7$

Putting in the equation

$y-y_1 = -7(x-x_1)$

Now we have to put a point in the equation, putting (3,6) in the equation

$y-6 = -7(x-3)$

Hence,

The required equation of line in point-slope form is:

$y-6 = -7(x-3)$