We have been given the equation and asked to graph a line to match the function. Let's first identify our -intercept, the value for when Now we know that is part of our graphed line. Next, we should consider from the equation. What does tell us? It tells us that with each new value, the line increases by units. This is the slope of the line. We can also think of it like this: every time we move by unit to the right, the line increases by units. Let's graph the line.
Unlike Part A, there is no way to find the -intercept for this line. We can choose for our function to start anywhere along the -axis. What we do know is that, the line will decrease by units for every units we move to the right. Our slope can be written as: Let's assume that the -intercept is and graph our line.
This function, will be graphed in a very similar way to the equation in Part A. This is because, although it is written with function notation, we can still find the -intercept and the slope. Recall that the -intercept it the value of the function when Here we have: From the function, we can also see that for each new value of there is only an increase by In other words: every time we move unit to the right, our function increases by unit. Let's graph this line.
We are not given information that would help us find the intercept for this line. We can, however, use the given and to find the slope of the line. But wait! We can't divide by zero, that's just not possible. This means that our line is not a function. There is no change in so we have a vertical line. Let's see what this looks like in a coordinate plane.