Chapter Five — Graphing Linear Equations in Two Variables
The Humongous Book of Algebra Problems
88
According to the table of values, the points (3,–5) and (24,9) belong to the
graph but (–12,–1) does not.
5.16 Through which of the following points, if any, does the graph of 3x – 5y = 2
pass?
A = (–10,–16); B = (4,–2); C = (39,23)
Use the method outlined in Problem 5.15—solve the equation for y, create a
table of values containing x = –10, x = 4, and x = 39, and compare the results
from the table with the y-coordinates in the given points.
A linear
graph that’s not
vertical only has
one y-value that goes
with each x-value. In
this case, the table of
values says when
x = –12, y = –15.
Therefore, the graph
can’t contain the
point (–12,1) as
well.
Chapter Five — Graphing Linear Equations in Two Variables
The Humongous Book of Algebra Problems
89
Because the coordinate pair C = (39,23) matches the values generated in the
last row of the table, point C belongs to the graph of 3x – 5y = 2.
5.17 If the graph of the line x – 2y = 10 passes through the points (8,a) and (b,3),
what is the value of a + b?
If the line x – 2y = 10 passes through the point (8,a), then substituting x = 8 and
y = a into the equation produces a true statement. Similarly, substituting x = b
and y = 3 into the equation also produces a true statement.
Solve the left equation for a and the right equation for b.
If a = –1 and b = 16, then a + b = –1 + 16 = 15.
Don’t try and
get creative and
look for underlying
meaning in the
expression a + b. Just
gure out what a and
b are by plugging them
into the equation and
then add them
together at the
end.
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