>> Welcome to a lesson on verifying ordered pairs, satisfy a given linear equation.
In example 1 we're asked to verify
that the ordered pairs below satisfy the equation yequals2x plus 3.
Yequals2x plus 3 is what's called a linear equation in 2 variable.
It's actually a linear equation in what's called slope intercept form
or the form y equals mx plus b. Notice in our case m equals 2 and b equals 3.
It's called a linear equation because if we were to graph 2 or more ordered pair
that satisfy this equation, it would form a straight line where all the points
on that line have ordered pairs that satisfy the linear equation.
When we have linear equation written in terms of x
and y. X is the input variable, and y in the output variable.
So to verify these ordered pairs satisfy the linear equation,
because the first value is the input and the second value is the output,
we'll substitute the first value for x and then the second value for y to verify the left side
of the equation equals the right side.
If it does, the ordered pair is a solution.
If it doesn't, it's not.
So for here we'll substitute negative 1 for y and negative 2 for x.
That would give us negative 1 equals 2 times negative 2 plus 3.
Again, we substituted negative 2 for x
and we substituted negative 1 for y. And now we simplify.
So on the right side we have 2 times negative 2, that's negative 4, and then plus 3.
And notice that -4 +3 is -1.
This is true, which verifies this ordered pair does satisfy a linear equation.
The next ordered pair is 0, 3.
So we'll substitute 0 for x and 3 for y. So we'd have 3 equals 2 times 0 plus 3.
Simplifying, we have 3 equal 0 plus 3.
So we have 3 equals 3, which is true,
which verifies this ordered pair satisfies our linear equation.
And finally we have the ordered pair 1,5.
So you substituted 1 for x and 5 for y. That would give us 5 equals 2 times 1 plus 3.
5 equals, well 2 times 1 of course is 2, and 2 plus 3 equals 5.
This is true, which again verifies the ordered pair satisfies a linear equation.
Now let's graph these 3 ordered pairs on the coordinate plane,
and verify they do form a straight line.
So we'll first plot the ordered pair negative 2, negative 1.
So we'd go left 2 and down 1 to here.
This is the ordered pair negative 2, negative 1.
Next we have the ordered pair 0,3, which would be on the vertical access here.
And then finally we have 1,5.
So we'd go right 1 up 5 to here.
This is the point with the ordered pair 1,5.
And notice how we can form a straight line through these 3 points,
which is the reason why this is called a linear equation.
Every single point on this line has an ordered pair that would satisfy the linear equation.
Example 2 we have the same question.
But now our equation is 3x plus 2y equals 6.
This is also a linear equation, 2 variables.
But this is what is called standard form, or the form ax plus
by equals c. Notice here a equals 3, b equals 2 and c equals 6.
But just like last time, the input variable is x and the output variable is y.
So for the order pair negative 2,6, we'll substitute negative 2 for x and positive 6 for y
to verify this ordered pair is a solution.
So we'd have 3 times negative 2 plus 2 times 6 equals 6.
Simplifying we multiply first.
We have negative 6 plus 12 equals 6.
Negative 6 plus 12 is 6.
6 equal 6 is true, which verifies this ordered pair satisfies the linear equation.
Next we have the ordered pair 0,3.
So we substitute 0 for x and 3 for y. So you'd have 3 times 0 plus 2 times 3 equal 6.
Well 3 times 0 is 0, 2 times 3 is 6, 0 plus 6 is 6.
This is true, verifying the ordered pair satisfies a linear equation.
Notice how this would be a point on the vertical axis or the vertical intercept.
And then here we have the ordered pair 2,0.
So we substitute 0 for y and 2 for x. So we'd have 3 times 2 plus 2 times 0 equals 6.
On the left we have 3 times 2 is 6, plus 2 times 0 is 0,
6 plus 0 of course is 6, 6 equals 6 is true.
Once again verifying the ordered pair satisfies our linear equation.
Let's graph these 3 ordered pairs on the coordinate plane
and verify they form a straight line.
So first we have the ordered pair negative 2,6, so left 2 and up 6.
Here. And next we have the ordered pair 0,3.
This point here on the vertical axis.
Again this is the vertical intercept.
Then we have the point 2,0 which would be on the horizontal axis here.
This is the horizontal intercept.
Once again notice how these 3 points form a straight line, which should always be the case
if we have ordered pairs that satisfy a linear occasion.
Okay, I hope you found this helpful. ------------------------------c1323e0b14b8--