Find the angular coefficient of the line represented by \(2y - 3x = 6\).

Find the angular coefficient of the line represented by \(2y - 3x = 6\).

• A. \(-\frac{3}{2}\)
• B. \(\frac{1}{2}\)
• C. \(-\frac{3}{4}\)
• D. \(\frac{3}{2}\)

Answer: (D)

To find the angular coefficient (or slope) of the line represented by the equation \(2y - 3x = 6\), we need to first rearrange this equation into the slope-intercept form, which is \(y = mx + b\), where \(m\) is the angular coefficient. Starting with the given equation: \[ 2y - 3x = 6 \] We can isolate \(y\) by following these steps: 1. Add \(3x\) to both sides: \[ 2y = 3x + 6 \] 2. Next, divide every term by \(2\) to solve for \(y\): \[ y = \frac{3}{2}x + 3 \] From this form, we can clearly see that the angular coefficient, or slope \(m\), is \(\frac{3}{2}\). This coefficient tells us how much \(y\) changes for a unit change in \(x\): for every increase of 1 in \(x\), \(y\) increases by \(\frac{3}{2}\). Thus, the angular coefficient of the line represented by the equation \(2y -

To find the angular coefficient (or slope) of the line represented by the equation (2y - 3x = 6), we need to first rearrange this equation into the slope-intercept form, which is (y = mx + b), where (m) is the angular coefficient.

Starting with the given equation:

[

2y - 3x = 6

]

We can isolate (y) by following these steps:

1. Add (3x) to both sides:

[

2y = 3x + 6

]

2. Next, divide every term by (2) to solve for (y):

[

y = \frac{3}{2}x + 3

]

From this form, we can clearly see that the angular coefficient, or slope (m), is (\frac{3}{2}). This coefficient tells us how much (y) changes for a unit change in (x): for every increase of 1 in (x), (y) increases by (\frac{3}{2}).

Thus, the angular coefficient of the line represented by the equation (2y -