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To find the equation of a line passing through a given point \((x_1, y_1)\) and with a given slope \(m\), we can use the point-slope form of a line:

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

In this case, the point is \((3, 5)\) and the slope is 2. Plugging these values into the equation:

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

Simplifying this equation:

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

Adding 5 to both sides:

\[
y = 2x - 1
\]

Thus, the equation of the line is:

\[
y = 2x - 1
\]

Would you like any further details or have any questions?

Here are 5 related questions to explore further:
1. How can you derive the slope-intercept form from the point-slope form?
2. What happens to the line if the slope is negative?
3. How would the equation change if the point was different but the slope remained the same?
4. How can you determine the slope of a line if you only have two points?
5. How do parallel and perpendicular lines relate to slopes?

**Tip:** In linear equations, the slope represents the rate of change, while the intercept indicates where the line crosses the y-axis.

What is the equation of the line that passes through the point (3, 5) and has a slope of 2?

Learn how to find the equation of a line passing through the point (3, 5) with a slope of 2. This step-by-step guide covers key algebraic concepts, such as using the point-slope formula. Ideal for students in Grades 7-10.

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