Algebra II: Coordinate Planes

Question

How do you find the equation of the line on a coordinate plane?

the line goes from 6 down to negative 6 slashing through -3.

Answer 1

Use the formula for a line:

y = mx + b

where m is the slope and b is the y-intercept. All you need to find m and b are two points on the line, (x₁, y₁) and (x₂, y₂):

m = (y₂ - y₁) / (x₂ - x₁)

If you can read the y-intercept off the graph, then just use that value for b. Otherwise plug the value in for m that you got into the line formula, then plug in y = y₁ and x = x₁ and solve for b.

EXAMPLE:

Given the points (3, 6) and (6, 0) find the equation of the line.

m = (y₂ - y₁) / (x₂ - x₁) = (0 - 6) / (-4 - 2) = (-6) / (6 - 3) = (-6) / (3) = -2

y = -2x + b

6 = -2(3) + b (Plugged in (3, 6) for x and y. You can use either given point)

6 = -6 + b

12 = b

y = -2x + 12