Linear Equations

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope represent in a linear equation?

Back

The slope represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is.

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the value of y when x is 0. It is the point where the line crosses the y-axis.

Front

How do you find the initial value in a linear equation?

Back

The initial value is found by identifying the y-intercept (b) in the equation y = mx + b.

Front

What is the rate of change in a linear relationship?

Back

The rate of change is the same as the slope (m) of the linear equation, indicating how much y changes for a unit change in x.

Front

What does it mean if the slope is negative?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship between the two variables.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How can you determine if a point lies on a line represented by a linear equation?

Back

To determine if a point (x, y) lies on the line, substitute the x-value into the equation and see if the resulting y-value matches the y-coordinate of the point.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input (x-value) has exactly one output (y-value).

Front

What is a table of values in relation to linear equations?

Back

A table of values lists pairs of x and y values that satisfy a linear equation, showing the relationship between the two variables.