(-2,6) (4,-3) rewrite in standard form

Question

I need help with solving this problem because I. Don’t get it at all

Answer 1

I am assuming you want to write the equation of a line passing through those points:

 

The standard form of an equation is Ax + By = C

 

 

Solve for the slope of the equation:

m = (Y2-Y1)/(X2-X1)

m = (-3 - 6)/(4 - 2)

m = -9/6 = -3/2

 

Solve for y-intercept by substituting one of the points into the point slope form:

y = mx + b

6 = (-3/2)*(-2) + b

6 = 3 + b                  subtract 3 from both sides of the equation

b = 3

 

Rewrite the point slope form using b:

y = mx + b

y = (-3/2)x + 3

 

Rewrite in standard form:

y = (-3/2)x + 3

y + (3/2)x = 3            Add (3/2)x to both sides of the equation

2(y + (3/2)x) = 2(3)   Multiply both sides by 2 to remove the fraction

2Y + 3X = 6               Rearrange to have X first, but its the same.

 

SOLUTION:  3X + 2Y = 6

 

You can check the solution by plugging in the points give:

 

Point (-2,6):

3(-2)+ 2(6) = 6

- 6 + 12 = 6

6 =6                   Correct!

 

Point (4,-3):

3(4) + 2(-3) = 6

12 - 6 = 6

6 = 6                 Correct!