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, where the change in one variable is proportional to the change in another.

Front

What is the general form of a linear equation?

Back

The general 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 of a line given two points?

Back

The slope (m) can be calculated using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What does the slope of a linear function represent?

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 unit change in x.

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

Back

A relationship is linear if the graph forms a straight line, indicating a constant rate of change between the variables.

Front

What is the significance of the equation t = -15w + 275 in the context of a water tank?

Back

This equation represents the total gallons of water (t) in the tank after w weeks, showing a linear decrease in water volume over time.

Front

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

Back

You can use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the formula for converting a slope-intercept form to standard form?

Back

To convert from slope-intercept form (y = mx + b) to standard form (Ax + By = C), rearrange the equation to get all terms on one side.

Front

What does the equation y = 5x represent in a real-world context?

Back

This equation represents a direct proportionality between y and x, such as the cost of pecans per pound, where y is the total cost and x is the weight in pounds.