Any point on a graph has two coordinates. For example, point A on the graph
shown has coordinates (2,4), which means that if you start at the origin and want
to get to A, you have to go 2 units to the right and 4 units up. For point A, 2 is
called its “x-coordinate” and 4 is called its “y-coordinate.” Point B has
coordinates (–1,–3).
The next element of coordinate geometry is a line, which connects and
extends through two points. Like so:
And as soon as we have a line, we also have a formula for that line, usually in
the form y = mx + b. For example, the line to the left has the formula y = (^7 / 3 )x +
(–⅔). Our m is (^7 / 3 ) and our b is (–⅔). But what are m and b? The easier one to
explain is b, which is our y-intercept, or the y-coordinate of the point where the
line hits the y-axis. Just take a look at that line. At which point does it cross the
y-axis? At (–⅔). So far, so good.
m stands for slope.* The slope of a line is an indication of how steep it is. To
figure out the slope of a line that connects two points (x 1 , y 1 ) and (x 2 , y 2 ), you use
the formula:
So, in our line above,