Was this the only possible line that goes through the points and ?
Yes. The line is unique.
No. There is exactly one more line possible.
No. There are a lot of lines that go through and .
No. There are an infinite number of lines that go through and .
Answer.
A
(Discussion could include that we would have to make the line curve to connect the points in more than one way. But, a line has to have the same slope everywhere.)
Letβs say you are given a table that listed six points that are on the same line. How many of those points are necessary to use to graph the line?
One point is enough.
Two points are enough.
Three points are enough.
You need to plot all six points.
You can use however many you want.
Answer.
B
Discussion could include pointing out that only two are necessary, but we can include more if we want. Also, including more is a good way to catch an error in plotting. One will stick out!
In Activity 3.3.3, we were given at least two points in each question. However, sometimes we are not directly given two points to graph a line. Instead we are given some combination of characteristics about the line that will help us find two points. These characteristics could include a point, the intercepts, the slope, or an equation.
Recall from Definition 3.2.14 that the equation of a horizontal line has the form where is a constant and a vertical line has the form where is a constant.