## Introduction

The point-slope form of a line is generally represented as y=mx+b, where m is the slope and b is the y-intercept. To write the point-slope form of the line passing through 2,12 and parallel to y=3x, we need to calculate the slope first. To do this, we take any two points on the line and use the formula m=(y2-y1)/(x2-x1). In this case, we would use points (2,12) and (3,15). Plugging these values into our formula gives us a slope of 3. Now that we have our slope, we can plug it into our general equation to get y=3x+b. Now, all that’s left to do is to calculate b by plugging in one of our points and solving for b. We’ll use (2,12) again. Plugging this into our equation gives us 12=3(2)+b, which simplifies to b=6. Therefore, our final equation is y=3x+6.

## What is the point-slope form?

The point-slope form is a way of writing the equation of a line that passes through a certain point and has a certain slope. The point-slope form is written as:

y – y1 = m(x – x1)

Where:

y is the y-coordinate of any point on the line,

y1 is the y-coordinate of the given point,

m is the slope of the line, and

x1 is the x-coordinate of the given point.

## How to write the point-slope form of a line

The point-slope form of a line is used when you are given the slope of a line and a point on that line, and you want to find the equation of the line. The point-slope form is:

y – y1 = m(x – x1)

Where m is the slope and (x1, y1) is the given point.

To use this form, simply plug in the slope and the coordinates of the given point, and solve for y. Then, use y = mx + b to put the equation into slope-intercept form.

## Examples

The point-slope form of a line is:

y – y1 = m(x – x1)

where m is the slope of the line and (x1, y1) is a point on the line.

For example, the point-slope form of the line passing through (2, 12) and parallel to y = 3x is:

y – 12 = 3(x – 2)

## Conclusion

The point-slope form of a line is y-y1=m(x-x1) where m is the slope of the line and (x1,y1) is a point on the line. The slope of the line y=3x-2 is 3 and the point (2,12) is on the line, so the equation of the line you are looking for is y-12=3(x-2).