Final answer:
To solve the given equations for the correct linear model, each equation is isolated for y to get them into the y = mx + b form. The solutions are: y = (4/3)x + 2, y = -(4/3)x + 2, y = (3/4)x - (3/2), y = -(3/4)x - (3/2).
Step-by-step explanation:
To solve the given linear equations and find the correct linear model, we'll work with each equation individually. We have four equations:
- 4x - 3y = -6
- 4x + 3y = 6
- 3x - 4y = 6
- 3x + 4y = -6
These equations need to be rearranged into the linear form y = mx + b, where m represents the slope and b represents the y-intercept.
For equation (a), 4x - 3y = -6, we can solve for y:
3y = 4x + 6
y = (4/3)x + 2
For equation (b), 4x + 3y = 6, solving for y yields:
y = -(4/3)x + 2
Similarly, for equation (c), 3x - 4y = 6, rearranging we get:
y = (3/4)x - (3/2)
And for equation (d), 3x + 4y = -6, solving for y yields:
y = -(3/4)x - (3/2)
Each of these equations is a linear model that could represent a relationship between the variables x and y.