Question

Given the equation y - 4 = three fourths (x 8) in point-slope form, identify the equation of the same line in standard form?

1) - three fourths x y = 10
2) 3x - 4y = -40
3) y = three fourths x 12
4) y = three fourths x 10

Answer 1

The given equation in point-slope form does not directly match any of the provided multiple-choice options in standard form. After converting the given equation into standard form, the result is 3x - 4y = 8, which is structurally closest to option 2, but not identical.

Step-by-step explanation:

The given equation y - 4 = ¾(x - 8) is initially in point-slope form. To convert this into standard form AX + BY = C, where A, B, and C are integers and A is non-negative, we can follow these steps:

• Multiply both sides by 4 to eliminate the fraction: 4(y - 4) = 3(x - 8).
• Distribute through the parentheses: 4y - 16 = 3x - 24.
• Bring all terms involving variables to one side and constants to the other: -3x + 4y = -24 + 16.
• Simplify the constant term: -3x + 4y = -8.
• Because standard form prefers the x-coefficient to be positive, multiply the entire equation by -1: 3x - 4y = 8.

Now, we compare the transformed standard form equation with the given multiple-choice options. The correct equation in standard form that represents the same line as the point-slope form given is:

3x - 4y = 8

However, none of the options listed exactly matches this equation. The correct standard form is not provided among the options, but the closest in structure is option 2.