Find the slope and the equation for the line passing through the points: (0,3) and (−1,−3).

Answer 1

One of the standard ways of writing and equation for a line is the slope-intercept method:

y = m*x + b where m is the slope and b is the y-intercept

However, we don't have either (yet). What we need to use is the point-slope method:

y - y_o = m * (x - x_o) where (x_o, y_o) is a point on the line.

We are not given the slope but can easily calculate it. The slope is the rise of the line (how much it goes up or down) divided by the run (how much it goes sideways). We have two points: P_o at (0, 3) and P₁ at (-1, -3). Moving from point P₁ to point P_o, we go right 1 unit and up 6, so our slope is m = 6/1 = 6 so we get

y - 3 = 6 * (x - 0)

or

y - 3 = 6x

so

y = 6x + 3

which gives us the slope intercept form of the line.