Write the equation of line m in standard form.

Question

Line m passes through C(-2,0) and D(1,-3). Write the equation of line m in standard form.

Answer 1

 

Standard form of a line is  Ax + By = C   where A,B,and C are constants.   

 

Other forms of equations for straight lines:

Point-slope:     y-y1 = m(x-x1)      (m = slope, (x1,y1) is a point on the line)

Slope-intercept:    y = mx + b     (m = slope,  b = y intercept)

 

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Given the line passes through  C(-2,0)  and D(1,-3) we can calculate the slope as  (y2-y1)/(x2-x1)

(you can choose either point to be (x1,y1), then the other point is (x2,y2)):  I will use C as (x2,y2)

and D as (x1,y1):

 

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

 

Now lets temporarily write the line in point-slope form:

                y - (-3) = -1*(x - 1)

                   y + 3 = -x + 1

                   y =  -x - 2

 

 In Standard Form, the x and y are together on the left side:    y + x = -2

 

 

 

 

Answer 2

Equation of line m in standard form is y-y1 = m(x-x1)

 

Slope m = y2-y1/(x2-x1) 

 

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

 

Now the line is,

 

y - 0 = -1(x+2)

 

y = -x - 2