Linear Relationships

Front

What is the definition of 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

How do you calculate the slope of a line given two points?

Back

The slope (m) of a line passing through two points (x1, y1) and (x2, y2) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What does the slope of a line represent in a linear relationship?

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 unit change in x.

Front

What is the y-intercept in the equation of a line?

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 is the equation of a line in slope-intercept form?

Back

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

Front

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

Back

A table of values represents a linear relationship if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

What is the significance of a slope of 0?

Back

A slope of 0 indicates a horizontal line, 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

How do you write the equation of a line given its slope and a point on the line?

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 formula for converting a linear equation from standard form to slope-intercept form?

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y: y = (-A/B)x + (C/B).