how to find the standard form and slope intercept form for points (-2/5.2/5) and (4/3,2/3)

Question

I am having trouble distributing the fractions. I have determind that the equation for standand form is:

y-2/5=2/9(x+2/5)

I know that I am supposed to clear the fractions but which one first and I need to see the step by step solution so I can understand to solve a different problem that looks like this.

I know that the answer is supposed to be 2x-13y=-6 according to my book

Answer 1

First, let's find the slope:

slope = (y2 - y1) / (x2 - x1)

slope = (2/3 - 2/5) / (4/3 - -2/5)

slope = (10/15 - 6/15) / (20/15 + 6/15)

slope = (4/15) / (26/15)

slope = 4 / 26

slope = 2/13

.

Now we do point-slope form:

y - y1 = m(x - x1)

y - 2/5 = (2/13)(x - -2/5)

y - 2/5 = (2/13)(x + 2/5)

(note: this is the equation you wrote in the post; it's only off a bit on the slope part)

y - 2/5 = (2/13)x + 4/65

(-2/13)x + y - 2/5 - 4/65 = 0

(-2/13)x + y - 26/65 - 4/65 = 0

(-2/13)x + y - 30/65 = 0

(-2/13)x + y - 6/13 = 0

-2x + 13y - 6 = 0

2x - 13y + 6 = 0

2x - 13y = -6