1. What is Slope?

Slope is a measure of the steepness of a line, representing the ratio of the vertical change (rise) to the horizontal change (run) between two points on a line. It describes both the direction and the steepness of the line.

2. How to Calculate Slope

The slope formula is:

Where:

• \( m \) — Slope (unitless)
• \( x₁ \) — x-coordinate of first point (unitless)
• \( y₁ \) — y-coordinate of first point (unitless)
• \( x₂ \) — x-coordinate of second point (unitless)
• \( y₂ \) — y-coordinate of second point (unitless)

Explanation: The formula calculates the ratio of vertical change to horizontal change between two distinct points on a line.

3. Finding Slope on TI-84 Calculator

Steps:

1. Press the "STAT" button
2. Select "Edit" and enter your x-values in L1 and y-values in L2
3. Press "STAT" again, move right to "CALC"
4. Select "LinReg(ax+b)"
5. The 'a' value displayed is the slope of your line

4. Using the Calculator

Tips: Enter the coordinates of two distinct points. The calculator will compute the slope using the formula m = (y₂ - y₁)/(x₂ - x₁). If the points form a vertical line (x₂ = x₁), the slope will be undefined.

5. Frequently Asked Questions (FAQ)

Q1: What does a positive slope indicate?
A: A positive slope indicates that the line is rising from left to right.

Q2: What does a negative slope indicate?
A: A negative slope indicates that the line is falling from left to right.

Q3: What does a slope of zero mean?
A: A slope of zero indicates a horizontal line with no vertical change.

Q4: Why is slope undefined for vertical lines?
A: Slope is undefined for vertical lines because the denominator (x₂ - x₁) becomes zero, and division by zero is undefined in mathematics.

Q5: Can slope be calculated with fractions or decimals?
A: Yes, the slope formula works with any real numbers including fractions and decimals.