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

y = -7x + 27 is the point slope equation that passes through the two points

Step-by-step explanation:

Here, we want to write the equation of the line between (3,6) and (5,-8)

Mathematically, the equation of the line that passes through both points can be represented by ;

y = mx + c

where m is the slope and c is the y-intercept

Let’s find the slope m first;

Mathematically;

slope m = y2-y1/x2-x1

where (x1,y1) = (3,6) and (x2,y2) = (5,-8)

Substitute these values in the slope equation , we have the following;

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

So the equation becomes;

y = -7x + c

we still need the value of c

To get this, we can substitute any of the points in the equation, where x is the x coordinate of the point and y is the coordinate of the point.

Let’s use (3,6)

Thus we have;

6 = -7(3) + c

c = 6 + 21

c = 27

So the equation becomes;

y = -7x + 27