Flashcard: TEKS 7.7 (Linear Relationships)

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph. It can be described by a linear equation of the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the dependent variable (y) with respect to the independent variable (x). It indicates how steep the line is and the direction it goes (positive or negative).

Front

What is the y-intercept in the equation y = mx + b?

Back

The y-intercept is the value of y when x is 0. It is represented by the 'b' in the equation y = mx + b.

Front

How do you find the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the equation of a line with a slope of 2 and a y-intercept of 3?

Back

The equation of the line is y = 2x + 3.

Front

If a line has a slope of 0, what does that indicate?

Back

A slope of 0 indicates that the line is horizontal, meaning there is no change in the y-value as the x-value changes.

Front

What does a negative slope indicate about a linear relationship?

Back

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

Front

What is the difference between a linear equation and a nonlinear equation?

Back

A linear equation represents a straight line and can be written in the form y = mx + b, while a nonlinear equation represents a curve and cannot be expressed in that form.

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 set of points forms a linear relationship?

Back

You can determine if a set of points forms a linear relationship by plotting them on a graph. If the points lie on a straight line, they represent a linear relationship.