Algebra Class: Rate of Change and Line Types

What is the slope of a line parallel to the equation $y = 3x + 4$?

Which of the following equations represents a line that is perpendicular to $y = 3x + 4$?

What is the equation of a line parallel to $y = 3x + 4$ that passes through the point (1,2)?

Which statement is true about horizontal and vertical lines?

What is the product of the slopes of two perpendicular lines?

What is the slope of a horizontal line?

Which line equation is a valid example of a line with an undefined slope?

Which of the following equations defines a line that is parallel to $y = 5$?

What is the slope of the line represented by the equation $y = 2x + 3$?

Which of the following represents a vertical line?

What is the standard form of the equation $y = 3x - 1$?

If a baby elephant weighs 210 pounds at birth and gains 28 pounds per week, what will its weight be after 3 weeks?

What is the formula for finding the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$?

In the point-slope form of a line, $y - y_1 = m(x - x_1)$, what does 'm' represent?

If the equation of a line is $2x + 5y = 12$, what would be its y-intercept?

During a snowstorm, how much snow was on the ground after 11 hours if there was 19.25 inches?

Rate of Change

Rate of change can be represented in a table, equation, or graph.
In a table, find the change in y values (Δy) and the change in x values (Δx). The rate of change is Δy/Δx.
In an equation, the rate of change is the coefficient of 'x'.
On a graph, the rate of change is the slope of the line. Find two points on the line; calculate the slope (rise over run).
Given two points (x₁,y₁) and (x₂,y₂), the slope formula is (y₂ - y₁)/(x₂ - x₁).
In an example, a baby elephant weighed 210 pounds at birth, and gained 28 pounds per week. This is represented by the equation y = 2x +3, where x is the number of weeks, and y is the weight of the elephant

Horizontal Lines

Horizontal lines have a slope of zero.
The equation of a horizontal line is of the form y = # (where # is a constant).

Vertical Lines

Vertical lines have an undefined slope.
The equation of a vertical line is of the form x = # (where # is a constant).

Slope-Intercept Form

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Example: y = 3x - 1, where the slope is 3 and the y-intercept is -1.

Standard Form

The standard form of a linear equation is Ax + By = C, where A, B, and C are constants, and A is non-negative.
Example: 2x + y = -4.

Point-Slope Form

The point-slope form of a linear equation is y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line.
Example: y - 3 = 5(x + 4).

Parallel Lines

Parallel lines have the same slope.
Parallel lines can have different y-intercepts.

Perpendicular Lines

Perpendicular lines have slopes that are negative reciprocals of each other (product of slopes is -1).
Perpendicular lines can have the same y-intercept.

Line of Best Fit

A line of best fit represents the trend or relationship between data points.
Calculated using methods like least-squares.
Use the slope and y-intercept calculated from the data to construct the line of best fit.
This line is used for prediction, not just to connect the data points.

This quiz covers the concepts of rate of change in algebra, including how to represent it in tables, equations, and graphs. Participants will learn about the characteristics of horizontal and vertical lines, as well as the slope-intercept form. Test your understanding of these essential algebraic principles.