Download Every straight line can be represented by an equation: y = mx + b

Two POINTS make a LINE
We can connect two points with a straight line.
Every straight line can be represented by an equation: y = mx + b. The
coordinates of every point on the line will solve the equation if you
substitute them in the equation for x and y.
The equation of any straight line, called a linear equation, can be written as:
y = mx + b, where m is the slope of the line and b is the y-intercept.
The y-intercept
of this line is the value of y at the point where the
line crosses the y axis.
m
1
To graph the equation of a line, we plot at least two points whose
coordinates satisfy the equation, and then connect the points with a line. We
call these equations "linear" because the graph of these equations is a
straight line.
There are two important things that can help you graph an equation, slope
and y-intercept.
Slope
We're familiar with the word "slope" as it relates to mountains. Skiers and
snowboarders refer to "hitting the slopes." On the coordinate plane, the
steepness, or slant, of a line is called the slope. Slope is the RATIO of the
change in the y-value over the change in the x-value. Carpenters and
builders call this ratio the "rise over the run." Using any two points on a line,
you can calculate its slope using this formula.
Let's use these two points to calculate the slope m of this line.
A = (1,1) and B = (2,3)
Subtract the y value of point A from the y-value of point B to find the
change in the y value (2 – 1), which is 2. Then subtract the x value of point
A from the x value of point B to find the change in x (3 – 1), which is 1. The
slope is 2 divided by 1, or 2.
When a line has positive slope, like this one, it rises from left to right.
When a line has positive slope, like this one, it rises from right to left.
Let's look at another line. This line has a negative slope, it falls from left to
right. We can take any two points on this line and find the slope. Let's take C
(0, -1) and D (2, -5).
Using these two points, we can calculate the slope of this line. We subtract
the y value of point C from the y value of point D, and the x value of point C
from the x value of point D, and divide the first value by the second value.
The slope is -2.
Y-Intercept
There's another important value associated with graphing a line on the
coordinate plane. It's called the "y intercept" and it's the y value of the point
where the line intersects the y- axis. For this line, the y-intercept is
"negative 1." You can find the y-intercept by looking at the graph and seeing
which point crosses the y axis. This point will always have an x coordinate
of zero. This is another way to find the y-intercept, if you know the equation,
the y-intercept is the solution to the equation when x = 0.
Equations
Knowing how to find the slope and the y-intercept helps us to graph a line
when we know its equation, and also helps us to find the equation of a line
when we have its graph. The equation of a line can always be written in this
form, where m is the slope and b is the y-intercept:
y = mx + b