Question

A line passes through (2, –1) and (8, 4). a. Write an equation for the line in point-slope form. b. Rewrite the equation in standard form using integers

Answer 1

The point-slope form of a line is:

y-y1=m(x-x1),  where m=slope and (x1,y1) is any point on the line

First we need to find the slope, which is (y2-y1)/(x2-x1)

m=(4--1)/(8-2)

m=5/6 and we can use either point, I'll use (8,4)

y-4=(5/6)(x-8)

That is your equation in point-slope form.

Now the standard equation of a line is ax+by=c

y-4=(5/6)(x-8)  we can perform the indicated multiplication on the right side

y-4=(5x-40)/6  multiply both sides by 6

6y-24=5x-40  add 24 to both sides

6y=5x-16  subtract 5x from both sides

-5x+6y=-16  and by convention, the standard equation of a line should be expressed with a positive coefficient for x, so multiply both sides by -1

5x-6y=16