standard form equation for this (5,1) (-3,4)

Question

I need help with this I cant figure out how to find the standard form for this so if you could help me with this than I would be very happy!!!

Answer 1

The point-slope form for the equation of a line is:   y-y₁ = m(x-x₁)  and the slope is m=(y₂-y₁)/(x₂-x₁), so the Standard Form of an equation of a line given 2 points is:   mx-y=mx₁-y₁   (looks like Ax+By=C)

                ((y₂-y₁)/(x₂-x₁))x - y = ((y₂-y₁)/(x₂-x₁))x₁ - y₁

                 (4-1)/((-3)-5)x - y = ( (4-1)/((-3)-5) )(5) - 1      [just use the two points]

                    (-3/8)x - y = -15/8 - 1

                      3x + 8y = 23                         (multiply both sides by -8)

 

p.s., this approach will become very handy in later math.

               

Answer 2

The two-point form can be used: (y - y₁)/(x - x₁) = (y₁ - y₂)/(x₁ - x₂)

 

(y - 1)/(x - 5) = (1 - 4)/(5 - (-3))       simplify

(y - 1)/(x - 5) = (-3)/(8)                    multiply both sides by (x - 5)

y - 1 = -3(x - 5)/8                             multiply both sides by 8

8(y - 1) = -3(x - 5)                           simplify

8y - 8 = -3x + 15                             add 8 to both sides

8y = -3x + 23                                  add 3x to both sides

3x + 8y = 23

 

 

Answer 3

First we need to find the slope:

m = (y₂-y₁)/(x₂-x₁)

m = (4-1)/(-3-5)

m = 3/-8

m = -3/8

 

Now we need to find the y intercept:

y = m*x+b

y = (-3/8)*x + b

1 = (-3/8)*5 + b

1 = -15/8 + b

1 + 15/8 = b

b = 23/8

 

Now this is what we have:

y = (-3/8)*x+23/8

 

To have a function in standard form, we do not want any fractions.  So we must multiply the entire equation by 8:

8y = -3*x+23

 

Now add 3x to both sides:

3x+8y = 23

 

Which is our standard form