what is the equation of the line that passes through the given points

Question

what is the equation of the line that passes through the given points (-2,-2) and (4,-4)

Answer 1

Ann, I will help you with this one and then you can do the other!

 

First, we need to find our slope.  In this case, it is (y₂ - y₁)/(x₂ - x₁).  Either of your points can be 1 or 2, as long as you go in the same direction.

 

Let's do (-4 - (-2))/(4 - (-2)) = -2/6 = -1/3

 

Now, we use the formula y - y₁ = m(x - x₁).  The x and y stay just x and y, but the x₁ and y₁ come from either point.

 

So, y - (-2) = -1/3(x - (-2))

 

y + 2 = -1/3x - 2/3

 

Subtracting 2 from both sides, we get y = -1/3x - 8/3

 

Hope this helps!

Answer 2

There are many different ways to come up with an equation of a line. When you are given two points and asked to find a line that passes through them the easiest way is with the point-point form.

y-y₁ = m(x-x₁) where m is the slope

To calculate the slope, think rise over run (change in y-values over change in x-values)

m=Δy/Δx = (-2-(-4))/(-2-4) = 2/-6 = -1/3

 

Then, plug in a point for (x₁,y₁)... Any given point will do.

y-(-2) = (-1/3)(x-(-2))

 

Then, it is all about simplifying

y+2 = (-1/3)(x+2)

y=(-1/3)(x+2) - 2

y=(-1/3)x - 2/3 - 2

y=(-1/3)x - 8/3

 

Hope this helps,

Chris