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Math Question: 4x - 3y = -10

by Jan
(Prescott, AZ)










































Linear Equation

   • The Standard form of a Linear Equation is shown below:

              4x - 3y = -10

          Graph the equation

          Rewrite the equation in:

             Slope–intercept form

             Point–slope form

             Two-point form

             Intercept form

Comments for Math Question: 4x - 3y = -10

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Sep 29, 2012
4x - 3y = -10
by: Staff


Answer:


Part I


Graph the equation:



Math – graph of 4x - 3y = -10






Standard form:

      Ax + By = C

           A = 4

           B = -3

           C = -10

      4x - 3y = -10


Slope–intercept form:

      y = mx + b

           4x - 3y = -10

           4x - 3y + 3y = -10 + 3y

           4x + 0 = 3y - 10

           4x = 3y - 10

           4x + 10 = 3y + 10 + 10

           4x + 10 = 3y + 0

           4x + 10 = 3y

           3y = 4x + 10

           3y / 3 = (4x + 10) / 3

           y * (3/ 3) = (4x + 10) / 3

           y * (1) = (4x + 10) / 3

           y = (4x + 10) / 3

           y = 4x * (1/3) + 10* (1/3)

           y = (4/3)*x + 10/3

           m = 4/3

           b = 10/3

      y = (4/3)*x + 10/3

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Sep 29, 2012
4x - 3y = -10
by: Staff


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Part II

Point–slope form:

      y - y₁ = m(x - x₁)

           y = (4/3)*x + 10/3

           y₁ = (4/3)*x₁ + 10/3

           y - y₁ = [(4/3)*x + 10/3] - [(4/3)*x₁ + 10/3]

           y - y₁ = (4/3)*x + 10/3 -(4/3)*x₁ - 10/3

           y - y₁ = (4/3)*x - (4/3)*x₁+ 10/3 - 10/3

           y - y₁ = (4/3)*x - (4/3)*x₁+ 0

           y - y₁ = (4/3)*x - (4/3)*x₁

           y - y₁ = (4/3)*(x - x₁)

      y - y₁ = (4/3)*(x - x₁)


Two-point form:

      y - y₁ = [(y₂ - y₁)/(x₂ - x₁)] * (x - x₁)

           (x1, y1) and (x2, y2) are different two points on the graph of the equation 4x - 3y = -10

           [(y₂ - y₁)/(x₂ - x₁)] is the slope “m”, by definition.

      y - y₁ = [(y₂ - y₁)/(x₂ - x₁)] * (x - x₁)


Intercept form:

      x/a + y/b = 1

          4x - 3y = -10

          (4x - 3y) / (-10) = (-10) / (-10)

          (4x - 3y) / (-10) = 1

          (4x) / (-10) + (-3y) / (-10) = 1

          (x) / (-10/4) + (y) / (10/3) = 1

          a = -10/4

          b = 10/3

      x/(-10/4) + y/(10/3) = 1



Thanks for writing.

Staff
www.solving-math-problems.com


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