Question 1

How do I calculate slope?

Accepted Answer

Use the formula m = (y2 - y1) / (x2 - x1). Subtract the y-coordinates (rise) and divide by the difference in x-coordinates (run). For points (2, 3) and (6, 11): m = (11 - 3) / (6 - 2) = 8 / 4 = 2. This means the line rises 2 units for every 1 unit it moves right.

Question 2

What does a slope of 0 mean?

Accepted Answer

A slope of zero means the line is perfectly horizontal. There is no vertical change between any two points on the line. The equation is y = b (a constant). For example, the line through (1, 5) and (7, 5) has slope 0 and equation y = 5.

Question 3

What is an undefined slope?

Accepted Answer

An undefined slope occurs when the line is vertical (x1 = x2), making the denominator zero in the slope formula. Vertical lines cannot be expressed as y = mx + b because they have infinitely steep rise. Instead, they are written as x = a constant, such as x = 3.

Question 4

How do I find the y-intercept from two points?

Accepted Answer

First calculate the slope m = (y2 - y1) / (x2 - x1). Then use point-slope form with either point: b = y1 - m x x1. For points (2, 5) and (4, 9): m = (9-5)/(4-2) = 2, then b = 5 - 2 x 2 = 1. The equation is y = 2x + 1.

Question 5

How are slope and angle of inclination related?

Accepted Answer

The angle of inclination (theta) is the angle the line makes with the positive x-axis. The relationship is m = tan(theta), or theta = arctan(m). A 45-degree angle gives slope 1, a 135-degree angle gives slope -1, and a 0-degree angle gives slope 0. Vertical lines have a 90-degree angle of inclination.

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