What is the slope of the line 2kx - (k+1)y : 3?

The given equation is \( 2kx - (k + 1)y = 3 \). To find the slope of this line, we need to rearrange it into the slope-intercept form of a linear equation, which is \( y = mx + b \), where \( m \) represents the slope.

### Steps to find the slope:
1. Start with the original equation:
   \[
   2kx - (k + 1)y = 3
   \]

2. Isolate \( y \):
   \[
   -(k + 1)y = -2kx + 3
   \]

3. Divide by \(-(k + 1)\) to solve for \( y \):
   \[
   y = \frac{2kx}{k + 1} - \frac{3}{k + 1}
   \]

4. Simplify this expression:
   \[
   y = \left(\frac{2k}{k + 1}\right)x - \frac{3}{k + 1}
   \]

### Slope:
The slope \( m \) is the coefficient of \( x \) in the equation \( y = mx + b \). Here, the slope \( m \) is:
   \[
   m = \frac{2k}{k + 1}
   \]

So, the slope of the line \( 2kx - (k + 1)y = 3 \) is \( \frac{2k}{k + 1} \).

Would you like further details or have any questions?

### Related Questions:
1. What happens to the slope when \( k = 0 \)?
2. How does the slope change as \( k \) approaches infinity?
3. What is the y-intercept of the line \( 2kx - (k + 1)y = 3 \)?
4. For what value of \( k \) is the slope of this line equal to 1?
5. How would you find the x-intercept of this line?

### Tip:
When finding the slope of a line from a linear equation, always try to rearrange the equation into the slope-intercept form \( y = mx + b \) for easy identification of the slope.

What is the slope of the line 2kx - (k+1)y = 3?

Learn how to find the slope of the linear equation 2kx - (k + 1)y = 3. This step-by-step solution explains how to rearrange the equation into slope-intercept form and calculate the slope using the formula m = 2k / (k + 1). Ideal for students in Grades 9-11.

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