Determine the equation of the line with a gradient of -4 and passing through point (2;-8)

To determine the equation of a line, we use the point-slope form of the equation of a line:

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

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

Given:
- Gradient \( m = -4 \),
- Point \( (x_1, y_1) = (2, -8) \).

Substituting into the point-slope form:

\[
y - (-8) = -4(x - 2)
\]

Simplifying:

\[
y + 8 = -4(x - 2)
\]

Expanding the equation:

\[
y + 8 = -4x + 8
\]

Now, subtract 8 from both sides to isolate \( y \):

\[
y = -4x + 8 - 8
\]

\[
y = -4x
\]

Thus, the equation of the line is:

\[
y = -4x
\]

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. What is the y-intercept of the line \(y = -4x\)?
2. How would you find the x-intercept of the line?
3. How do you graph a line given its equation?
4. What happens if the gradient of a line is positive?
5. How do you write the equation of a vertical line?

**Tip:** The slope tells you how steep the line is. A negative slope means the line goes down as you move from left to right.

Determine the equation of the line with a gradient of -4 and passing through point (2, -8)

Discover how to find the equation of a line with a slope of -4 passing through the point (2, -8). This step-by-step guide covers the use of point-slope and slope-intercept formulas, making it ideal for Grades 8-10 students learning about linear equations.

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