Question

Write the standard form of the equation for the line represented by the equation: y - 2 = -3/4 (x + 4).

A) 3x + 4y = 8
B) 4x - 3y = -2
C) 3x - 4y = -8
D) 4x + 3y = 2

Answer 1

4y + 3x = - 4

Step-by-step explanation:

y - 2 = -3/4 (x + 4)

Lets rearrange to standard form of y = mx + b, where m is the slope and b is the y-intercept (the value of y when x is equal to zero).

y - 2 = -3/4 (x + 4)

y - 2 = -(3/4)x - 3 [Expand parentheses]

y = -(3/4)x - 1 [Add 2 to both sides]

We'll rearrange this to match one of the answer options.

y = -(3/4)x - 1

4y = -3x - 4 [Multiply both sides by 4]

4y + 3x = - 4

This is not an answer option.

Answer 2

The standard form of the equation is 3/4x + y = -1.

Step-by-step explanation:

The given equation is y - 2 = -3/4 (x + 4). To write it in standard form, we need to eliminate the fractions and rearrange the terms. First, distribute -3/4 to the terms in parentheses: y - 2 = (-3/4)(x) + (-3/4)(4). Simplifying, we have y - 2 = -3/4x - 3. Now, add 3/4x to both sides to get rid of the negative coefficient: 3/4x + y - 2 = -3. Lastly, rearrange the terms to put the equation in standard form: 3/4x + y = -3 + 2. Combining like terms, we get 3/4x + y = -1. Therefore, the standard form of the equation is 3/4x + y = -1 (Option D).