We're asked to find four ordered pair solutions
to the given equation by completing the table
then graph the line.
The equation is y equals negative five x plus four.
Looking into the first row,
we are given x equals negative one.
To find the corresponding y value,
we substitute negative one for x
and solve for y.
Performing this substitution gives us y equals
negative five times x, but x is negative one,
giving us negative five times negative one,
and then we have plus four.
Simplifying on the right side,
negative five times negative one is positive five,
and five plus four is equal to nine.
When x is negative one, y is nine.
One ordered pair solution is negative one, comma, nine.
In the next row, we are given y equals negative 11,
which now we substitute negative 11 for y
and solve for x.
Performing the substitution
gives us the equation negative 11 equals
negative five x plus four.
The first step is to add or subtract
to isolate the variable term.
To undo the plus four, we subtract four on both sides.
Simplifying,
negative 11 minus four is negative 15.
On the right, four minus four is zero.
The right side simplifies to negative five x.
The next step is to multiply or divide to solve for x.
Negative five x means negative five times x.
To undo the multiplication and solve for x,
we divide both sides by negative five.
Simplifying, negative 15 divided by negative five is three.
On the right, negative five divided by itself simplifies
to one, one times x is x.
Three equals x is equivalent to x equals three.
When y is negative 11, x is equal to three.
The ordered pair solution is three, comma, negative 11.
In the next row, x equals two.
When x equals two,
y is equal to negative five times two plus four.
Simplifying, negative five times two is negative 10,
and negative 10 plus four is equal to negative six.
When x is two, y is negative six.
The ordered pair solution is two, comma, negative six.
And for the last row, we are given y equals four.
Substituting y for four gives us four
equals negative five x plus four.
First step, isolate negative five x
by subtracting four on both sides.
Simplifying, four minus four is zero.
We have zero equals on the right,
four minus four is zero again.
The right side simplifies to negative five x.
The last step to solve for x
is to divide both sides by negative five.
Simplifying, zero divided by negative five is zero.
On the right, negative five divided by itself simplifies
to one, one times x is x.
Zero equals x is equivalent to x equals zero,
which means when y is four, x is zero.
The ordered pair solution is zero, comma, four.
And now to graph the line,
we will graph these four points on the coordinate plane,
and if we found these ordered pairs correctly,
a line will pass through all four points.
To plot the point negative one, comma, nine from the origin,
we move left one unit and then up nine units.
For three, comma, negative 11,
from the origin, we move right three
and then down 11 units.
The next ordered pair solution is two, comma, negative six.
From the origin, we move right two units
and then down six units.
The last ordered pair is zero, comma, four from the origin.
We do not move left or right.
We only go up four units,
and the graph of the linear equation
is the line passing through these four points.
I hope you found this helpful.