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Find the equation of the line given the following conditions.

4. Slope = 2, passing through (3, 5)

To find the equation of a line given the slope and a point through which it passes, we use the point-slope form of a line's equation:

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

Where:
- \(m\) is the slope,
- \((x_1, y_1)\) is the point through which the line passes.

Given:
- Slope \(m = 2\),
- Point \((x_1, y_1) = (3, 5)\).

Substituting these values into the point-slope formula:

\[
y - 5 = 2(x - 3)
\]

Now, let's simplify this equation:

\[
y - 5 = 2x - 6
\]

Add 5 to both sides:

\[
y = 2x - 1
\]

Thus, the equation of the line is:

\[
y = 2x - 1
\]

Would you like further details or clarification?

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Here are 5 related questions for further exploration:
1. How can we rewrite the equation of a line in standard form?
2. What is the y-intercept of the line from this equation?
3. How would the equation change if the slope were negative?
4. Can you find the equation of a line parallel to this one but passing through a different point?
5. How can you verify if a point lies on this line?

**Tip:** The point-slope form is particularly useful when you know a point and the slope of the line.

Find the equation of the line given the following conditions. 4. Slope = 2, passing through (3, 5)

Learn how to find the equation of a line with a slope of 2 passing through the point (3, 5). The solution demonstrates the use of the point-slope form and simplifies it to the slope-intercept form, suitable for students in Grades 8-10.

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