Question

The point-slope form of the equation of the line that passes through (-4, -3) and (12, 1) is y−1=4(x−12). What is the standard form of the equation for this line?

a) x−4y=−8
b) 0x−4y=2
c) 4x−y=8
d) 4x−y=2

Answer 1

The standard form of the equation provided is 4x - y = 47, which does not match any of the given choices, suggesting a possible typo in the initial point-slope form or an error in the answer choices.

Step-by-step explanation:

The standard form of a linear equation is often written as Ax + By = C, where A, B, and C are integers, and A is non-negative. To convert the point-slope form of the equation y - 1 = 4(x - 12) to standard form, we first distribute the 4 to obtain y - 1 = 4x - 48. After that, we can add 1 to both sides to obtain y = 4x - 47. Subsequently, subtracting 4x from both sides yields -4x + y = -47. Multiplying the entire equation by -1 to get a positive x coefficient and to match one of the given choices results in 4x - y = 47, which does not match any of the given choices. Therefore, either there is a typo in the point-slope form provided, or none of the answer choices are correct.