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, typically expressed in 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 much y changes for a one-unit increase in x.

Front

How do you determine if a relationship is proportional?

Back

A relationship is proportional if it can be represented by a straight line that passes through the origin (0,0). In a proportional relationship, the ratio of y to x is constant.

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 equation of a line given a slope and a point?

Back

You can use the point-slope form of the equation: y - y1 = m(x - x1), where (x1, y1) is the point on the line and m is the slope.

Front

What is the difference between a proportional relationship and a non-proportional relationship?

Back

A proportional relationship passes through the origin and has a constant ratio between y and x, while a non-proportional relationship does not pass through the origin and may have a different ratio.

Front

How can you identify the slope from a graph?

Back

The slope can be identified by selecting two points on the line and calculating the rise (change in y) over the run (change in x) between those points.

Front

What does the equation y = mx + b represent?

Back

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

Front

How do you convert a linear equation from standard form to slope-intercept form?

Back

To convert from standard form (Ax + By = C) to slope-intercept form (y = mx + b), solve for y in terms of x.

Front

What is the significance of the slope being positive or negative?

Back

A positive slope indicates that as x increases, y also increases, while a negative slope indicates that as x increases, y decreases.