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 described by the equation y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.HSF-LE.A.1B

Front

What does the slope of a linear equation represent?

Back

The slope of a linear equation 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.

Tags

CCSS.8.EE.B.5

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 two points?

Back

To find the equation of a line given two points (x1, y1) and (x2, y2), first calculate the slope (m) using m = (y2 - y1) / (x2 - x1). Then use the point-slope form of the equation: y - y1 = m(x - x1) to find the equation.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How can you determine if a relationship is linear from a graph?

Back

A relationship is linear if the graph of the data points forms a straight line. This indicates a constant rate of change between the variables.

Tags

CCSS.8.F.A.3

Front

What is the significance of the coefficients in the equation y = mx + b?

Back

In the equation y = mx + b, 'm' represents the slope of the line, indicating the steepness and direction, while 'b' represents the y-intercept, indicating where the line crosses the y-axis.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

What does a negative slope indicate about a linear relationship?

Back

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

Tags

CCSS.8.EE.B.5

Front

How do you interpret the y-intercept in a real-world context?

Back

In a real-world context, the y-intercept represents the initial value of the dependent variable when the independent variable is zero, providing a starting point for the relationship.

Tags

CCSS.HSF.LE.B.5

Front

What is the relationship between parallel lines and their slopes?

Back

Parallel lines have the same slope but different y-intercepts. This means they will never intersect.

Tags

CCSS.8.EE.B.5