Tables: 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 (m) represent in a linear equation?

Back

The slope (m) 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 y-intercept (b) in a linear equation?

Back

The y-intercept (b) is the value of y when x is 0. It represents the starting point of the line on the y-axis.

Front

How do you identify a linear equation from a table of values?

Back

To identify a linear equation from a table, check if the change in y is consistent for equal changes in x. If the differences are constant, the relationship is linear.

Front

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

Back

The equation is y = 2x + 3.

Front

If a table shows that y increases by 4 when x increases by 2, what is the slope?

Back

The slope is 2, calculated as (change in y) / (change in x) = 4 / 2.

Front

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

Back

A negative slope indicates that as the independent variable (x) increases, the dependent variable (y) decreases, showing an inverse relationship.

Front

How can you determine the equation of a line from two points?

Back

To determine the equation, first calculate the slope (m) using the formula m = (y2 - y1) / (x2 - x1). Then use one of the points to solve for the y-intercept (b) and write the equation in the form y = mx + b.

Front

What is the significance of the point (0, b) on a graph?

Back

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

Front

What does it mean for a relationship to be proportional?

Back

A proportional relationship is a specific type of linear relationship that passes through the origin (0,0), meaning that the ratio of y to x is constant.