Find the equation of the line with gradient 5 passing through (2, 13)

To find the equation of the line with gradient (slope) \( m = 5 \) that passes through the point \( (2, 13) \), we can use the **point-slope form** of a line:

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

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

Given:
- \( m = 5 \),
- \( (x_1, y_1) = (2, 13) \),

Substitute these values into the point-slope form:

\[
y - 13 = 5(x - 2)
\]

Now, simplify the equation:

\[
y - 13 = 5x - 10
\]

\[
y = 5x - 10 + 13
\]

\[
y = 5x + 3
\]

Thus, the equation of the line is:

\[
y = 5x + 3
\]

Would you like more details or have any questions?

Here are five related questions to extend your understanding:
1. What is the equation of the line with gradient \( -2 \) passing through \( (4, -1) \)?
2. How do you find the y-intercept of a line given its slope and a point on the line?
3. Can you convert the equation \( y = 5x + 3 \) into standard form \( Ax + By = C \)?
4. How would you find the slope of a line given two points on the line?
5. What is the slope of a line parallel to the line \( y = 5x + 3 \)?

**Tip:** Always remember that the slope of parallel lines remains the same.

Find the equation of the line with gradient 5 passing through (2, 13).

Learn how to find the equation of a line with a slope of 5 that passes through the point (2, 13). This step-by-step solution explains the point-slope form and simplifies the equation to slope-intercept form y = 5x + 3. Suitable for students in Grades 8-10.

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