Question

Which of the following is the equation of a line that passes through the points (0,6) and (2,10)?

Answer 1

To construct an equation of that kind you either need y - y1 = m(x -x1) or y = mx + c; where m is the gradient and (x1, y1) are a set of coordinates on the graph. Note that the first will take the form of the second in anycase.

If you have a y-intercept (the place the graph crosses the y-axis) you don't need the first equation as you are then given the y-intercept: c

You always have a y-intercept at x = 0 so we know c = 6 from the coordinates (0, 6)

Now we need the gradient m which is given by (y1 - y2)/(x1-x2) where (x1, y1) & (x2, y2) are sets of coordinates i.e (0, 6) and (2, 10). Remember that it doesn't matter which set of coordinates you choose as (x1, y1) or (x2, y2) as the answer will be the exact same. So choosing x1 = 0 and thereby making y1 = 6 we have the equation

(6 - 10)/(0 - 2) = -4/-2 = 2
so m = 2

Using y = mx +c
we have the equation y = 2x + 6