Question

Writing equations in standard form:

Hi I need help with writing equations in standard form using points. The points are (4,5) and (-3,-1) I already found the slope which is 6/7 but I don’t know how to do the point slope form. This is the slope form if you don’t know:
Y-y1=m(x-x1)

Answer 1

You have already done half of it. Now substitute for x1 = 4 and y = 5
y - 5 = 6/7(x - 4)
Multiply everything by 7 to remove fractions
7y - 35 = 6(x - 4)
7y - 35 = 6x - 24
-6x + 7y = -24 + 35
-6x + 7y = 11

Some people prefer a positive number in front of x so multiply by -1
6x - 7y = -11

You can check the answer by testing it works for both of the original points
6x4 - 7x5 = 24 - 35 = -11 true
6x-3 - 7x-1 = -18 - -7 = -11 true