Linear Equations

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Linear Equations

• Algebra II Chapter Two
• Robert Conyer

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The X-axis is the horizontal line on the
coordinate plane. X is usually some form of time
(seconds, minutes, months, years, etc..). X is
the independent variable. The Y-axis is the
vertical line on the coordinate plane. Y is
dependent variable. The value of Y is determined
by the value of X. The value of Y depends on the
value of X. In the table above, there is a
distinct pattern. When there is a distinct
pattern in a table, the table represents a linear
equation. A linear equation is an equation that
forms a straight line when it is graphed on the
coordinate plane. A linear equation can be
recognized in two forms. Slope-intercept form
and Standard form.
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Slope-Intercept Form Y MX B (M The
Slope, B Y-intercept) The Y-intercept is the
location where the line crosses the Y-axis. In
this graph the Y-intercept is 0. The Slope is
represented by letter M. Slope is how
far the line rises or falls between two points
over how far the line runs (travels) to the left
or right between two points. You can find the
slope of a line by first determining how far the
line goes up between two points (5 is the rise on
the graph). Second, determine how far the line
runs between two points (1 is the run on the
graph). The slope for this graph is 5 over 1 or
.
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Find the pattern in the table to determine the
slope. The pattern is Y increases by five as X
increases by one. The pattern in Y is plus five.
Place a five next to X (5X). Next, replace the
X with a one and multiply one and five. The
product is five. This proves that the
slope-intercept form for this table is Y 5X
0. The zero represent the Y-intercept.
The pattern in this table is plus three. Place a
three next to X (3X). Substitute one for X and
multiply. The product is three. Three plus four
equals seven. The slope-intercept form for this
table is Y 3X 4. The slope (M) equals
three. The y-intercept is four.
The value of Y when X equals zero is the
Y-intercept. When X is zero, Y is four. Four is
the Y-intercept.
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The graph and the table can be used to determine
the slope-intercept form. Both the graph and the
table show that the Y-intercept is four. The
value of Y when X equals zero is four on the
table. The point where the line crosses the
Y-axis is four on the graph. The graph rises by
three spaces and runs one space to the right.
The pattern in the table is plus three. Place 3
with X (3X). Substitute one for X and multiply.
The product is 3. Add 4 and 3 and the sum is 7.
Slope-intercept form for this graph and table
is Y 3X 4.





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