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Graphing a Linear Relation Involving Fractions.
Create a table of values and graph the
linear relation y equals one half x plus 3.
So, let's calculate the values of y, y equals one half x plus 3.
Substitute in the values of x into this equation.
Y equals one half times negative 2 plus 3.
One half times negative 2 equals negative 2 over 2 plus
3, which equals negative 1 plus 3, which equals 2.
So when x equals negative 2, y equals 2.
Next, let's substitute in the value for x equals
negative 1, y equals one half times negative 1 plus 3.
Which equals negative one half plus 3, which equals, to add fractions you
must have a common denominator, negative one half plus some number over 2.
When you have a number 3 by itself it's understood to be over 1.
So, 1 times 2 is 2 and 3 times 2, in the numerator, is 6.
Add the numbers across the top, negative 1 plus 6 equals 5 over 2.
Which equals 5 divided by 2 in your calculator, 2.5.
So when x equals negative 1, y equals 2.5.
Next, let's substitute in the value for x equals 0.
Y equals one half times 0 plus 3.
Which equals 0 plus 3, which equals 3.
So when x equals 0, y equals 3.
Let's substitute in the value x equals 1, y
equals one half times 1 plus 3, which equals
one half plus 3, which equals 3.5.
So when x equals 1, y equals 3.5.
And next, let's substitute in x equals 2 into the equation.
Y equals one half times 2 plus 3, which
equals 2 over 2 plus 3, which equals 1 plus
3, which gives you a final answer of 4.
So when X equals 2, y equals 4.
Let's plot these points on the graph.
This is the x axis, and this is the y axis.
So are first point is negative 2 and positive 2.
Our next point is negative 1 and 2.5.
Our next point is 0 and 3.
Our
next point is 1 and 3.5.
And then 2 and 4.
Draw a straight line connecting these points.
Note, be sure to include negative and positive values for x in your table
of values, so that you get a
better representation of what the graph looks like.