One way to write linear function rules is in standard form.
Graph the linear function given by the equation using a table of values.
To draw the graph of the function, we can plot all five points in a coordinate plane and connect them with a line.
The intercepts of a graph share an important feature. For all -intercepts, the -coordinate is and for all -intercepts, the -coordinate is This can be used to find the intercepts of a graph when its rule is known. For example, consider the line given by the following equation.
To find the -intercept, can be substituted into the equation.Next, solve the equation for
The -intercept can be found in a similar way. Substitute into the equation and solve for
The amusement park ride "Spinning Teacups" has two different sizes of cups, large and small. Large cups fit people and small cups fit people. Maximum capacity for each ride is people. The equation models this situation, where is the number of small cups and is the number of large cups. Graph the situation and interpret the intercepts.
To graph the function, we can plot the intercepts in a coordinate plane, and connect them with a line.
Notice that the graph does not extend infinitely. This is because, since and represent the numbers of different cups, negative numbers should not be included.
We can interpret the intercepts in terms of what and represent. The -intercept is This means a ride with small cups can not have any large cups, because the maximum capacity of people has already been met. Similarly, the -intercept of tells us that a ride with large cups will not allow for any small cups.