Write the equation of the line that passes through the points (0,2) and (-1,-1):

Question

Write the equation of the line that passes through the points (0,2) and (-1,-1):

Answer 1

Equation of a line:

 

y = mx +b

 

Where;

m = slope

b = y-intercept

 

You are given the y-intercept from the point (0,2). When x = 0, y = 2

You can then see from the Eq: y = mx + b  

that b = 2

 

The slope, m is found by calculating the change in y over the change in x or "rise over run".

 

m = (y₁-y₂)/(x₁-x₂)

 

One of the points is (x₁, y₁) and the other (x₂, y₂)

 

 

m = (2-(-1)) / (0 -(-1)) = (2+1)/(0+1) = 3/1 = 3

 

So the Eq. for the line passing through the two points is;

 

y = 3x + 2

Answer 2

Melissa,

 

Let's start with the point-slope form:

 

(y - y₁) = m(x - x₁) where m is the slope.

 

First, find the slope m:

 

m = (y₂ - y₁)/(x₂ - x₁₎

 

m = (-1 - 2)/(-1 - 0)

 

m = -3/-1

 

m = 3

 

Now, using either coordinate (I'll use the first), the equation looks like this:

 

(y - 2) = 3(x - 0)

 

y - 2 = 3x

 

Add 2 to both sides:

 

y = 3x + 2 (the equation of the line in slope-intercept form where y = 2 is the y-intercept.