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Chapter — Graphng

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Linear Equations

Equations in two variables are classified by the exponent (power) of the variables. First degree equations,

that is, equations whose variables are raised to the first power, are

. That means that

linear equations

when these equations are graphed in the Rectangular Coordinate System, their graphs make a straight

line.

Linear equations fit a pattern that looks like Ax + By = C, where x and y are the variables and A, B, and C

are real number constants with A and B not both equal to zero. Ax + By = C is called the

standard form

equation of a line.

y

For example, the equation 2x + 3y = 10 is a linear equation

with infinitely many solutions; (2, 2), (5, 0), and (–1, 4)

are just a few of them. You can see from the graph of this

y-intercept

line (the figure at right) that solutions to a linear equation

(-1, 4)

(2, 2)

are points on the graph of that equation.

x-intercept

x and y-Intercepts

x

(5, 0)

There are two

that convey

ordered pair solutions

extra information and that have special names, the x- and

y-intercepts. The

is the point at which the

x-intercept

graph of the line crosses the x-axis. As you can see in the

figure at right, that point is (5, 0). It is important to note

that the y-coordinate of this point is zero. Similarly, the

is the point at which the graph of the line

y-intercept

crosses the y-axis. The x-coordinate at this point is zero. Though we have not plotted this point on the

graph of the line, you can see that it does exist at the point where the line crosses the y-axis.

The x and y-intercepts allow us to find two ordered pair solutions with minimal effort.

The point at which the line crosses the x-axis is the x-intercept at (x, 0).

The point at which the line crosses the y-axis is the y-intercept at (0, y).

y = mx + b: The Slope-Intercept Form of the Equation of a Line

There is a special form of the equation for a line that allows us to read information directly from it. The

for the equation of a line looks like y = mx + b. From the slope-intercept form

slope-intercept form

of an equation, we can determine two important pieces of information by inspection—just by reading the

equation.

y =

x +

m

b

The first is m, the coefficient of x. That value has special meaning

for the graph of the line. It is the

of the line, or how steep

slope

or inclined the line is. The value b in the slope-intercept form

slope

y-intercept

indicates the second piece of information, the y-intercept, which

is the point (0, b).

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Parent category: Education