Write the equation of the line passing through the point (2,5) with a slope of 3


To find the equation of the line that passes through the point \((2, 5)\) with a slope of \(3\), we can use the point-slope form of a line's equation:

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

Where:
- \(m\) is the slope of the line,
- \((x_1, y_1)\) is the point on the line.

Substituting the given point \((2, 5)\) and the slope \(m = 3\) into the equation:

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

Now, we can simplify this to get the slope-intercept form \(y = mx + b\):

\[
y - 5 = 3x - 6
\]

Add 5 to both sides:

\[
y = 3x - 1
\]

So, the equation of the line is:

\[
y = 3x - 1
\]

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you find the slope of a line given two points?
2. What is the general form of a linear equation?
3. How would you find the y-intercept of a line from its equation?
4. How do you convert a point-slope form equation to slope-intercept form?
5. What does the slope of a line represent geometrically?

**Tip:** Remember, the slope-intercept form \(y = mx + b\) is particularly useful for quickly identifying the slope and y-intercept of a line.

Learn how to write the equation of a line passing through the point (2, 5) with a slope of 3 using the point-slope form and converting it to slope-intercept form. This problem covers fundamental concepts in linear equations and is suitable for Grades 7-9.

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