How do i write an equation when given two points?

Question

Write the equation of the line through the points: (-3,16) (12,4)

Answer 1

m = (16-4)/(-3-12) = -4/5,

-4/5 = (y-4)/(x-12),

y = (-4/5)x + (68/5)

Answer 2

The first thing that you need to do to find the equation is find the slope of the line.

The equation for slope is: m = (y₂ - y₁)/(x₂ - x₁)

m = (4 -16))/(12 - (-3))       Substitute the values from the points into the slope formula

m = -12/15                         Simplify

m = -4/5                             Reduce the fraction

Once you have the slope, you can use the point-slope formula to find the equation.

The point slope formula is y - y₁ = m(x - x₁)

I am going to substitute the first point, but you will get the same answer with either point.

y - 16 = -4/5(x - (-3))              Point-slope formula with 1st point and slope substituted

y - 16 = (-4/5)x - 12/5             Distribute the -5/4

y = (-4/5)x - 12/5 + 16            Add 16 to each side

y = (-4/5)x -12/5 + 80/5          Find the common denominator to add fractions

y = (-4/5)x + 68/5                   Simplify