What is the equation of a line which passes through (-3, -14) and (4, 21)?

Answer 1

There are many ways to express the equation of a line but the most efficient with the given information is the "point-slope" formula (y - y₁) = m(x - x₁), where (x₁, y₁) is some point on the line and m is the slope of the line.

Since two points are given, we just need to pick one of them to get (x₁, y₁) so the only thing left to find is m.

Slope is "rise over run" or, expressed mathematically, m = (y₂ - y₁)/(x₂ - x₁). Plugging in the points from this problem we get m = (21 - -14)/(4 - -3) = 35/7 = 5.

Now just plug this information into the "point-slope" formula to get the equation of the line:

(y - 21) = 5(x - 4)

You could also have used the other point to get another equation:

(y + 14) = 5(x + 3)

These are both correct and describe the same line.

Finally, if you want to find the "slope-intercept" equation of the line (which is often how lines are reported and has a unique form), you can solve either of these for y, obtaining:

y = 5x + 1