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The problem asks to:

1. Write the point-slope form of the equation of the line with a given slope of 2, passing through the point (6, 3).
2. Convert the point-slope form into the slope-intercept form.

### Step 1: Point-slope form of a line
The point-slope form of a line is given by the formula:

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

Where:
- \( m \) is the slope (given as 2),
- \( (x_1, y_1) \) is a point on the line (given as (6, 3)).

Substitute the given values:

\[
y - 3 = 2(x - 6)
\]

This is the point-slope form of the equation.

### Step 2: Convert to slope-intercept form
To get the slope-intercept form \( y = mx + b \), simplify the equation:

\[
y - 3 = 2(x - 6)
\]

Distribute the 2:

\[
y - 3 = 2x - 12
\]

Now add 3 to both sides to isolate \( y \):

\[
y = 2x - 12 + 3
\]

\[
y = 2x - 9
\]

Thus, the slope-intercept form of the equation is:

\[
y = 2x - 9
\]

Would you like any more details or clarifications on this?

Here are 5 related questions to explore further:
1. What is the meaning of the point-slope form of a line?
2. How do you derive the slope-intercept form from the point-slope form?
3. How can you graph a line using the slope-intercept form?
4. What is the role of the slope in determining the steepness of a line?
5. How would you find the x- and y-intercepts of this line?

**Tip**: Always check your work by plugging the given point into the final equation to ensure it satisfies the equation of the line.

Write the point-slope form of the line's equation satisfying the given conditions. Slope = 2, passing through (6, 3). What is the point-slope form of the equation of the line? (Simplify your answer.)

Learn how to find the point-slope form of a line given a slope of 2 passing through the point (6, 3). Convert the point-slope form into slope-intercept form with a step-by-step solution. Suitable for students in Grades 8-10.

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