Question

Find an equation of a line that goes through the points (1,6) and (4, -2). Write your answer in the form y=mx + y.

Answer 1

The desired equation is y = (-8/3)x + 26/3.

Explanation:

Moving from (1,6) to (4, -2) involves an increase of 3 in x and a decrease of 8 in y. Thus, the slope of the line thru these two points is m = rise / run = -8/3.

Using the slope-intercept form of the eq'n of a straight line and inserting the data given (slope = m = -8/3, x = 4, y = -2), we get:

y = mx + b => -2 = (-8/3)(4) + b, or -2 = -32/3 + b

Multiply all terms by 3 to clear out the fraction:

-6 = -32 + 3b.

Then 26 = 3b, and b = 26/3.

The desired equation is y = (-8/3)x + 26/3.