Chapter Five — Graphing Linear Equations in Two Variables
The Humongous Book of Algebra Problems
98
The graph of Ax + By = C intersects the x-axis at and intersects the y-axis
at . Apply the slope formula to calculate the slope of the line containing
those points.
Rewrite the complex fraction as a quotient and simplify.
The slope of line Ax + By = C is .
5.38 Use the formula generated in Problem 5.37 to determine the slope of the line
with equation 3x = 6y + 5.
Subtract 6y from both sides of the equation 3x = 6y + 5 so that both of its
variable terms appear on the left side of the equation and the constant term is
isolated on the right side.
3x – 6y = 5
The equation is now in the form Ax + By = C, and you can calculate the slope of
the line using the shortcut formula.
This is a
handy shortcut,
as you’ll see in the
next problem.
Chapter Five — Graphing Linear Equations in Two Variables
The Humongous Book of Algebra Problems
99
5.39 Graph the line that passes through (–3,1) and has slope .
The slope of a line indicates the vertical and horizontal change between points
on the line. The numerator indicates vertical distance, and the denominator
indicates horizontal distance. Here, the slope is negative, so place the negative
sign either in the numerator or the denominator—your choice will not affect
the outcome.
Plot the given point (–3,1) on the coordinate plane. According to the slope
, if you travel down five units and right two units from that point, you arrive
at another point on the line. Because the slope is equivalent, you can also
travel up five units and left two units to reach another point on the line, as
illustrated by Figure 5-17. Connect the points to graph the line.
Figure 5-17: The point (–1,–4) is five units below and two units right of the starting
point (–3,1). The point (–5,6) is five units above and two units left of
(–3,1).
A positive
numerator
means “up,” and a
negative numerator
means “down.” A positive
denominator means
“right,” and a negative
denominator means
“left.”
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