Find the equation of the line whose slope is -3 and the x-intercept is 5. 

To find the equation of a line given the slope and the x-intercept, you can use the point-slope form of the equation:

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

Here, \( m \) is the slope, and \( (x_1, y_1) \) is a point on the line. Since you know the x-intercept, the point \( (x_1, y_1) \) will be \( (5, 0) \), because at the x-intercept, \( y = 0 \).

Given:
- Slope \( m = -3 \)
- Point \( (x_1, y_1) = (5, 0) \)

Substituting into the point-slope form:

\[
y - 0 = -3(x - 5)
\]

Simplifying the equation:

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

Expanding this:

\[
y = -3x + 15
\]

So, the equation of the line is:

\[
y = -3x + 15
\]

Would you like more details on how this was derived, or do you have any other questions?

Here are 5 related questions to deepen your understanding:
1. How do you find the y-intercept of the line given in the problem?
2. What is the equation of a line parallel to the one given but passing through a different point?
3. How would the equation change if the slope were positive instead of negative?
4. How can you determine the slope of a line if you're only given two points?
5. How would you graph the line \( y = -3x + 15 \) on the coordinate plane?

**Tip:** Remember, the slope \( m \) indicates how much \( y \) changes for every unit increase in \( x \). If the slope is negative, the line falls as it moves from left to right.

Find the equation of the line whose slope is -3 and the x-intercept is 5.

Discover how to find the equation of a line with a slope of -3 and an x-intercept of 5 using the point-slope and slope-intercept forms. Ideal for students in Grades 8-10, this problem explores key algebraic concepts and provides a step-by-step solution.

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