Write the equation of a line that is parallel to 
 
\[{y=-\dfrac{3}{2}x-1}\] and that passes through the point 
\[{(4,6)}\].


To find the equation of a line parallel to 

\[
y = -\frac{3}{2}x - 1
\]

and passing through the point \((4, 6)\), follow these steps:

### Step 1: Identify the Slope
Since parallel lines have the same slope, the slope of the new line will be the same as the slope of the given line. The slope of the given line \( y = -\frac{3}{2}x - 1 \) is:

\[
m = -\frac{3}{2}
\]

### Step 2: Use the Point-Slope Form
The point-slope form of a line is given by:

\[
y - y_1 = m(x - x_1)
\]

where \((x_1, y_1)\) is a point on the line, and \( m \) is the slope. Plugging in the point \((4, 6)\) and the slope \( m = -\frac{3}{2} \), we get:

\[
y - 6 = -\frac{3}{2}(x - 4)
\]

### Step 3: Simplify the Equation
Distribute \(-\frac{3}{2}\) on the right side:

\[
y - 6 = -\frac{3}{2}x + 6
\]

Then, add 6 to both sides:

\[
y = -\frac{3}{2}x + 12
\]

### Final Answer
The equation of the line parallel to \( y = -\frac{3}{2}x - 1 \) and passing through the point \((4, 6)\) is:

\[
y = -\frac{3}{2}x + 12
\]

Would you like more details on any step?

### Additional Questions to Explore
1. What would be the equation of a line perpendicular to the given line through \((4,6)\)?
2. How do you find the distance between two parallel lines?
3. How can you find the y-intercept of a line given the slope and a point?
4. How can we verify if two lines are parallel given their equations?
5. What is the general formula for the slope-intercept form of a line?

### Tip:
Remember, two lines are parallel if their slopes are equal.

Write the equation of a line that is parallel to y = -3/2x - 1 and that passes through the point (4, 6).

Find the equation of a line parallel to y = -3/2x - 1 that passes through the point (4, 6). This problem involves algebraic concepts including the point-slope form and properties of parallel lines, suitable for students in Grades 8-10.

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