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. It can be expressed in the form of an equation, typically y = mx + b, where m is the slope and b is the y-intercept.

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.

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 write the equation of a line given a slope and a point?

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 difference between dependent and independent variables?

Back

The independent variable is the variable that is manipulated or changed, while the dependent variable is the variable that is measured or affected in response to changes in the independent variable.

Front

How can you identify a linear relationship from a table of values?

Back

A linear relationship can be identified if the differences between consecutive y-values divided by the differences between consecutive x-values are constant.

Front

What is the equation for a linear relationship that starts with an initial amount and increases by a constant rate?

Back

The equation is typically in the form y = initial amount + rate of change * x.

Front

If a delivery service charges a flat fee plus a variable cost per mile, how is this represented in an equation?

Back

This is represented as c = flat fee + (variable cost per mile * m), where c is the total cost and m is the number of miles.

Front

What does it mean for a relationship to be proportional?

Back

A proportional relationship is a specific type of linear relationship that passes through the origin (0,0) and can be expressed as y = kx, where k is a constant.

Front

How do you graph a linear equation?

Back

To graph a linear equation, you can plot the y-intercept on the y-axis and use the slope to find another point. Then, draw a straight line through the points.