Linear Relationships

Front

What is a proportional relationship?

Back

A proportional relationship is a relationship between two quantities where the ratio of one quantity to the other is constant. For example, if one quantity increases, the other quantity increases at a consistent rate.

Front

How can you identify a proportional relationship from a word problem?

Back

Look for constant ratios or relationships where one quantity is a constant multiple of another. For example, if a hotel charges a flat rate plus a variable cost that is a constant amount per unit, it is not proportional.

Front

What is the slope of a line in the equation y = mx + b?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how much y changes for a unit change in x.

Front

How do you find the y-intercept in the equation of a line?

Back

The y-intercept is the value of y when x is 0. In the equation y = mx + b, the y-intercept is represented by b.

Front

What does the equation y = 1/3x - 2 represent?

Back

This equation represents a linear relationship where the slope is 1/3 and the y-intercept is -2.

Front

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

Back

Use the point-slope form of the equation: y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope.

Front

What is the significance of the slope in a real-world context?

Back

The slope indicates the rate of change between two variables. For example, in a cost scenario, it shows how much the total cost increases for each additional unit purchased.

Front

How can you determine the equation of a line from a table of values?

Back

Identify the slope by calculating the change in y over the change in x between two points, then use one of the points to find the y-intercept.

Front

What does the equation y = 3x + 5 represent?

Back

This equation represents a linear relationship with a slope of 3 and a y-intercept of 5.

Front

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

Back

The y-intercept represents the starting value of the dependent variable when the independent variable is zero.