Question

Write the standard form of a line that passes through (1, 1) and (3, 4)

Answer 1

Answer:

3x - 2y = 1

Step-by-step explanation:

Step 1:   Find the slope

slope m = (y2 - y1)(/x2 - x1)

 m = (4 - 1)/(3 - 1) = 3/2

Step 1:  Use the formula y = mx + b to solve

This is slope-intercept form of a line.  We have a slope of 3/2, and a point (x, y), which is (1, 1).  Plug those values into the equation above and solve for b (the only variable we are missing

1 = (3/2)(1) + b

   1 = 3/2 + b  

          1 - 3/2 = b

             2/2 - 3/2 = b

                  -1/2 = b

Step 2: Rewrite the formula using the slope and the b value we just calculated

 y = (3/2)x - 1/2

Step 3:  Standard form of a line is ax + by = c, where a is a positive integer, so we rearrange the equation from step 2 to standard form.  

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

 -(3/2)x + y = -1/2     (subtract (3/2)x from both sides)

 

      -3x + 2y = -1       (multiply by 2 to get rid of the fraction on x)

           3x - 2y = 1     (multiply by -1 so a becomes positive)