Question

Determine the value of the coefficient of x in the equation Ax + 6y = 8 when the graph of the line goes through the point (-2, 4). Write your equation standard form. (Rules for standard form: A is non-negative, and A, B, C should be integers, and A, B, C should not have a common factor)

Answer 1

To determine the value of the coefficient of x in the equation Ax + 6y = 8, rearrange the equation in standard form and substitute the point (-2, 4) into the equation. Solve for A and the coefficient.

Step-by-step explanation:

To determine the value of the coefficient of x in the equation Ax + 6y = 8, we need to identify the value of A. We can do this by rearranging the equation in standard form, which is Ax + By = C. In this case, we can rewrite the equation as x(A/6) + y(6/6) = 8/6. Simplifying this gives us x(A/6) + y = 4/3. Since the line passes through the point (-2, 4), we can substitute x = -2 and y = 4 into the equation to solve for A.

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

Now, we can multiply both sides of the equation by 6 to eliminate the fraction:

-2A + 24 = 8

Next, we can subtract 24 from both sides:

-2A = -16

Finally, dividing both sides by -2 gives us:

A = 8

Therefore, the coefficient of x in the equation Ax + 6y = 8 is 8.

Answer 2

After substituting the point (-2, 4) into the equation Ax + 6y = 8 and solving for A, the coefficient A is found to be 8. Dividing the entire equation by 2 gives the standard form equation 4x + 3y = 4, with no common factors and non-negative A.

Step-by-step explanation:

To determine the value of the coefficient A of x in the equation Ax + 6y = 8, when the graph passes through the point (-2, 4), you substitute the x and y values of the point into the equation:

Thus, A(-2) + 6(4) = 8.

Now simplify and solve for A:

-2A + 24 = 8

Subtract 24 from both sides:

-2A = 8 - 24

-2A = -16

Divide both sides by -2:

A = 8

Hence, the equation with A determined is 8x + 6y = 8. To write it in standard form, where A is non-negative and A, B, C are integers with no common factor, divide the entire equation by 2:

4x + 3y = 4

This is the equation in standard form, meeting all the requirements.