a Plot the points and the draw the line going through them. Then use the graph to find more points and identify their similarities.
B
b Plot the points and see what characterizes them.
C
c Plot the points and see what characterizes them. You can use what you learned from Part B.
A
aGraph:
Example Points: (3,1) and (3,3). Similarities between all points: While the y-coordinates changes the x-coordinate is always 3.
B
bGraph:
Equation: y = - 1
C
cExample Points: (5,4), (2,4) and (1,4)
Example Equation: y = 4
Practice makes perfect
a We will plot the points (3,-1), (3,2), and (3,4). Then we can the draw a line passing through them as required.
The exercise asks us to find two more points lying on the same line. From the graph we can identify the points (3,1) and (3,3). Of course, there are infinitely many points on the line and these are just examples.
After that, we are asked to identify what would be true for the coordinates of any point lying on this line. As we can see above, for all the points the x-coordinate is always 3 and the y-coordinate is the only one changing.
b Now we are asked to plot the points (5,- 1), (1, -1), and (-3,-1). Then we must find the equation for the line that goes through them.
Let's start by plotting the points and drawing the line joining them.
As we can see, the value of the y-coordinate never changes. It does not depends on x at all, it is always -1. Therefore the equation for this line is just y=- 1.
c The exercise asks to choose three points and find the equation of the line that goes through them. From what we saw before in Part B, when the y-coordinate does not change the equation of the line does not depend of the variable x at all. The equation is in the form y=a, where a is the constant value for the y-coordinate. We can easily construct an example solution using this information.
&Points: (5,4), (2,4) and (1,4)
&Equation: y = 4
Note there are infinitely many correct solutions, so we what we have illustrated is just one possibility.
