a If a point on the graph is a steps away from the x-axis, how many steps away from the y-axis does it have to be if the point should be equidistant from the x- and y-axes?
B
b In the second and fourth quadrant, the x- and y-values will be opposites of each other.
C
c Combine what you found in part A and part B.
A
a y=x
B
b y=- x
C
c y=|x|
Practice makes perfect
a If a graph is equidistant from the x- and y-axes, any point on the graph that is, say a units from the x-axis, should also be a units from the y-axis.
Let's find one more point that is equidistant from the x- and y-axes. This time, we will move - b units away from each axis which puts us in the third quadrant.
Finally, by drawing a line through these points, we get a graph that is equidistant from the x- and y-axes in the first and third quadrant.
The only equation that passes through the origin and gives the same y-coordinate as it's x-coordinate is
y=x.
b Let's graph two points, one in the second quadrant and one in the fourth quadrant. Following the same line of logic as in part A, we will plot them so that they are equidistant from the axes.
Finally, by drawing a line through these points, we get a graph that is equidistant from the x- and y-axes in the second and fourth quadrant.
The only equation that passes through the origin and gives a y-coordinate that is the opposite of the x-coordinate is:
y=- x.
c From part A, we know that the points on y=x are equidistant from the axes in the first and third quadrant. Similarly, from part B we know that the points on y=- x are equidistant from the axes in the second and third quadrant. If we combine y=- x in the second quadrant and y=x in the first quadrant, we get a graph where all the points are equidistant from the axes.
