Determine an equation of a line in slope-intercept form given two non-intercept points on the line

Question

Write the equation of the line, in slope intercept form, that passes through the points (-3,-12) (-18,-18)

Answer 1

When you are given two points and no other information, you have to begin with the point-slope form of the equation of a line.  That form is

 

y-y₁ = m(x-x₁) when (x₁,y₁) is one of your given points and m is the slope.  

 

You may recall that slope is

        y₂-y₁

m = -------

       x₂-x₁

 

Using the given points, we can determine the slope

 

       (-18)-(-12)       -6          2
m = ------------  = ------- = ----
        (-18)-(-3)      -15          5

 

Now we can use this slope in the point-slope formula

 

y-(-12) = (2/5)[x-(-3)]

y+12 = (2/5)x +(6/5)

 

Finally put this into the slope intercept form, y = mx + b

y = (2/5)x + (6/5) - 12

y = (2/5)x + (6/5) - (60/5)

y = (2/5)x - (54/5)