Understanding Linear Equations and Functions

A collection of flashcards to help understand linear equations, slopes, y-intercepts, and the domain of functions.

y = mx + b

The slope-intercept form of a linear equation, where m represents the slope and b represents the y-intercept.

Slope (m)

A measure of the steepness of a line, calculated as the ratio of the rise (change in y) over the run (change in x).

Rise over Run

A phrase used to describe the slope of a line, indicating how much the value rises for every unit increase in the horizontal direction.

Y-intercept (b)

The value at which a line crosses the y-axis, represented as the constant addition in the equation y = mx + b.

How to find the slope from a table of values?

Identify the change in y-values over the change in x-values between two points; this ratio represents the slope.

If m = 3, what does that imply about the slope?

For every 1 unit increase in x, y increases by 3 units.

What happens to the graph when b is changed?

Changing b modifies the y-intercept of the line, moving it up or down without changing its slope.

Domain of a function

The set of all possible input values (x-values) for which a function is defined.

What does it mean if x cannot equal 0 in a function?

The function has a vertical asymptote at x = 0, indicating that the function is undefined at this point.

Why do we use brackets in calculations?

To clarify the order of operations, especially when working with negative numbers and exponents.