Determine the standard form of the equation of the line that passes through (-8,-6) (-4,9)

Answer 1

Standard form = Ax + By = C

However, to create the equation, we will use y = mx+b and then convert it to standard form. We need slope = m and y intercept = b.

Find slope = rise / run = change in y / change in x

(-8,-6) and (-4,9)

y changes from -6 to 9 = up 15

x changes from -8 to -4 = right 4

slope m = 15/4

Find y intercept by choosing a point to plug in for x and y to solve for b. I am going to use (-4,9)

y = mx + b

9 = (15/4)*(-4) + b multiply 15/4 and -4

9 = -60/4 + b simplify -60 / 4

9 = -15 + b add 15 to both sides

y intercept 24 = b

Let’s set up y = mx + b

y = 15/4x + 24

To be in standard form:

1. the x and y need to be on the same side
2. x needs to be positive
3. there can’t be any fractions

y = 15/4x + 24 multiply everything by 4 to get rid of the fraction ( this will cancel out the /4 and just leave the 15)

4y = 15x + 96 now subtract 15x from both sides so x and y are on the same side

-15x + 4y = 96 lastly, x needs to be positive so we are going to flip the signs of everything (multiply everything by -1)

Standard Form

15x - 4y = -96