Linear Relationships Review

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

Front

What is the slope-intercept form of a linear equation?

Back

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

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 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

What does it mean if the slope of a line is negative?

Back

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

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

How can you determine if a relationship is linear from a table of values?

Back

A relationship is linear if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

What is the significance of the point (0, b) in a linear equation?

Back

The point (0, b) represents the y-intercept of the line, indicating where the line crosses the y-axis.

Front

If a line passes through the points (1, 3) and (4, 9), what is the slope?

Back

The slope is 2, calculated as (9 - 3) / (4 - 1).