Linear Equations and Their Interpretations

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

Back

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

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.

Front

What is the y-intercept of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of b in the equation y = mx + b.

Front

How can you determine if a relationship is linear from a scatter plot?

Back

A relationship is linear if the points on the scatter plot form a straight line or a pattern that can be approximated by a straight line.

Front

What is the purpose of a trend line in a scatter plot?

Back

A trend line helps to visualize the general direction of the data points and can be used to make predictions.

Front

How do you interpret the slope of a line in a real-world context?

Back

The slope represents the rate of change between the two variables; for example, in a wage problem, it shows how much money is earned per hour.

Front

What does it mean if there is no correlation in a scatter plot?

Back

No correlation means that there is no apparent relationship between the two variables; changes in one do not predict changes in the other.

Front

How do you predict a value using a linear equation?

Back

To predict a value, substitute the known value of x into the linear equation and solve for y.