Question

Help me check my work?

Write the equation of the line that goes through the points (-1, 3) and (4, -7) in general form.

Also, could you clearly show and explain each step, thanks in advance:)

Answer 1

general form: y=mx+b
equation for slope of a line:
m=rise/run
m=(y2-y1)/(x2-x1)
m=(-7-3)/(4-(-1))=-2
so..
y=-2x+b
now plug in one of the given points to solve for b, I chose (4,-7)
-7=-2(4)+b
b=1
so equation of the line is:
y=-2x+1

Answer 2

I tried it, and just wanted to make sure it was correct?

Since they asked for the answer to be in general form (which is standard form) of a line:

Ax + By = C where A is a positive integer, and B, and C are integers

First I found the slope between the two points:
m = (y2-y1)/(x2-x1)
m = (4-3)/(4-1)
m = 1/3 (slope)

Then I used one of the two points (1,3) and the slope (1/3) and plug it into the point-slope form:
y-y1 = m(x-x1)
y-3 = (1/3)(x-1)
multiplying both sides by 3:
3y-9 = x-1
subtracting x from both sides:
-x + 3y-9 = -1
adding 9 to both sides:
-x + 3y = 8

is that correct? it seems pretty correct to me

Answer 3

it looks correct

Answer 4

general form of a line is
y=mx+b if you want it in Ax+By=C form then it would be
y+2x=1
from the work I did above

Answer 5

oh wait. general form is Ax + By + C = 0

so would it then be
-x + 3y = 8 (+0)
-x + 3y - 8 = 0
?

Answer 6

I think you are using the wrong points for you y2, y1, x2, x1
y2=-7 y1=3 x2=4 x1=-1 use those and try to solve it again.
With the form you want the equation 2x+y-1=0