Which of the following ordered pairs
make the equation y equals negative five x plus three true?
Or which ordered pairs satisfy the equation?
Each ordered pair consists of two values
where the first value is the x value,
and the second value is the y value.
To determine which ordered pairs make the equation true,
we substitute the first value for x,
the second value for y,
and see if that makes the equation true,
or satisfies the equation.
So the first ordered pair is one comma negative one,
and therefore we substitute one for x,
and negative one for y.
Performing this substitution gives us negative one equals.
Remember, negative five x means negative five times x,
and because x is one, on the right side we have
negative five times one plus three.
And now we simplify the right side of the equation
following the order of operations.
So we multiply first, negative five times one
is negative five, which gives us negative one equals
negative five plus three.
Negative five plus three is negative two.
Negative one does not equal negative two,
which means the ordered pair does not make
the equation true, or does not satisfy the equation.
The next ordered pair is six comma negative 27,
so now we substitute six for x,
and negative 27 for y.
Performing this substitution gives us
negative 27 equals negative five times six plus three.
Simplifying, we have negative 27 equals on the right side.
Negative five times six is negative 30.
So we have negative 30 plus three.
Negative 30 plus three is negative 27.
This gives us negative 27 equals negative 27,
which is true, meaning the ordered pair is a solution,
and therefore we check this ordered pair as a solution.
The next ordered pair is negative seven comma 37.
We substitute negative seven for x, and 37 for y.
Performing this substitution gives us
37 equals negative five times negative seven plus three.
Simplifying, negative five times
negative seven is positive 35.
35 plus three is 38.
37 does not equal 38,
and therefore this ordered pair
does not make the equation true or is not a solution.
The next ordered pair is eight comma negative 35.
Performing the substitution for x and y,
we have negative 35 equals
negative five times eight plus three.
Simplifying the right side,
negative five times eight is negative 40,
and negative 40 plus three is negative 37.
Negative 35 does not equal negative 37,
and therefore this ordered pair
does not make the equation true
or does not satisfy the equation.
The last ordered pair,
we substitute five for x and negative 22 for y.
This gives us negative 22 equals
negative five times five plus three.
On the right side, negative five
times positive five is negative 25.
Negative 25 plus three is negative 22.
Negative 22 does equal negative 22,
which means this ordered pair does make the equation true,
and is a solution, and therefore we also check
the ordered pair five comma negative 22.
Another way to see if these ordered pairs
make the equation true or are solutions to the equation
would be to graph the line, and if the ordered pair
is a solution or makes the equation true,
the ordered pair would represent a point on the line.
So let's also look at this graphically before we go.
The linear equation y equals
negative five x plus three is graphed in blue.
Notice how all the points are close to being on the line,
but the only two points that are on the line
are the points given by the ordered pairs
five comma negative 22, and six comma negative 27.
Notice how this point, this point, and this point
are not on the line, which means they do not make
the equation true or are not solutions to the equation.
I hope you found this helpful.