Question 638348

1.
Find the slope of the line by dividing the change in y-coordinates by the change in x-coordinates: 

{{{slope = (y2 - y1)/(x2 - x1)}}}. 

For example, given the coordinates (2, 0) and (-1, 3), the {{{slope = (3 - 0)/(-1 - 2) = -1}}}.

If both of the x-coordinates equal some value {{{k}}}, the slope and y-intercept are undefined, and the equation for the line will be {{{x = k}}}.

2.

Calculate the y-intercept by multiplying the slope times one of the x-coordinates and subtracting the product from the y-coordinate of the same point: 

{{{y-intercept = y1 - slope*x1}}}, where {{{x1}}} and {{{y1}}} are coordinates of one of the given points. 

For example, knowing that the {{{slope = -1}}}, use the point (2, 0): {{{y-intercept = 0 - (-1)*2 = 2}}}.

3.

Write the equation for the line in the {{{slope-intercept}}} format: 

{{{y = slope*x + y-intercept}}}. 

In the given example, {{{y = -x + 2}}}.

4.

Verify the equation by plugging in the {{{x}}}- and {{{y-coordinates}}} of the given points. If the equation remains balanced after simplifying, your equation is good. 

For example, given the equation {{{y = -x + 2}}}, plug in the first point (2,0): 

{{{0 = -2 + 2}}}. That's true, so everything checks out so far. 

Try again with (-1, 3): 
{{{3 = 1 + 2}}}. That's true too, so the equation is good.