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

## How do i write an equation when given two points?

# 2 Answers

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

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

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

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 = (y_{2} - y_{1})/(x_{2} - x_{1})

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 - y_{1} = m(x - x_{1})

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

## Comments

Oops... I think you meant to say that the slope m = rise over run, or (y2-y1)/(x2-x1)

Thanks for correcting me on that.

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