Slope from two points on a trip step by step

What is slope?

Slope measures the steepness of a line, calculated as the vertical change divided by the horizontal change.

Formula for slope between two points.

The formula is $\displaystyle m = \\frac{y_2 - y_1}{x_2 - x_1}$, where $\displaystyle (x_1, y_1)$ and $\displaystyle (x_2, y_2)$ are the coordinates of the points.

What do you need to find slope?

You need the coordinates of two distinct points on a line, typically in the form $\displaystyle (x_1, y_1)$ and $\displaystyle (x_2, y_2)$.

True or false: Slope can be negative.

True, because a negative slope indicates the line descends from left to right.

Fill in the blank: The slope of a horizontal line is ____.

0, because there is no vertical change as you move along the line.

How to calculate slope from (2, 3) and (4, 7)?

Using the formula: $\displaystyle m = \\frac{7 - 3}{4 - 2} = \\frac{4}{2} = 2$.

Difference between positive and negative slope.

Positive slope rises from left to right, while negative slope falls from left to right.

Quiz question: What does a slope of 1 signify?

The line rises one unit vertically for every one unit it moves horizontally.

True or false: Slope is always a whole number.

False, because slope can be any rational number, including fractions.

Example of a slope scenario.

On a trip, if you climb 300 feet over 600 feet horizontally, the slope is $\displaystyle \\frac{300}{600} = 0.5$.

What is the slope if points are (3, 5) and (6, 8)?

The slope is $\displaystyle \\frac{8 - 5}{6 - 3} = \\frac{3}{3} = 1$.

What represents a steep slope?

A steep slope has a larger absolute value, indicating a greater change in vertical distance over horizontal distance.

How does slope affect a trip's path?

A steeper slope means a more challenging ascent or descent, impacting travel time and effort.

True or false: The slope can be zero.

True, a zero slope indicates a horizontal line, meaning no vertical change.

What do you find on a graph to determine slope?

Identify two points on the line, then use their coordinates to calculate the slope.

What is the slope of a vertical line?

Undefined, because vertical lines do not have a horizontal change ($\displaystyle x_2 - x_1 = 0$).

Fill in the blank: The slope of (1, 2) to (1, 5) is ____.

Undefined, as both points have the same x-coordinate.

What can slope tell us about a store's pricing strategy?

A positive slope in price vs. quantity sold indicates that as prices go up, quantity sold increases.

How is slope related to incline?

Slope indicates the steepness of an incline, with higher slopes representing steeper inclines.