Find the value of $B - A$ if the graph of $Ax + By = 3$ passes through the point $(-7,2),$ and is parallel to the graph of $x +
3y = -5.$
1 answer:
Answer:
-6
Step-by-step explanation:
The parallel line can be written using the same x- and y-coefficients, but with a different constant:
x +3y = constant
For the line to go through the given point, the constant must be ...
(-7) +3(2) = constant
-1 = constant
In order for the constant to be +3 instead of -1, the entire equation must be multiplied by -3:
-3x -9y = 3 ⇒ A = -3, B = -9
Then the expression B-A is ...
B -A = (-9) -(-3) = -6
The value of B - A is -6.
You might be interested in
A general linear equation is given by:
Where a is the slope and b is the y-intercept.
Here we will find that the linear equation that represents the situation is
And we can expect that the median salary in 2048 is $2.853 million
If the line passes through the points (x₁, y₁) and (x₂, y₂) then the slope can be written as:
Here we know that:
in 2007 (x = 7) the median player salary was y = $1.5 million
in 2013 (x = 13) the median player salary was y = $1.7 million.
Then we have two points that we can write as:
(7, 1.5)
(13, 1.7)
Note that the y-value is in millions.
Then the slope of the linear equation will be:
So the linear equation is something like:
To find the value of b, remember the point (7, 1.5), this means that when we have x = 7, we also have y = 1.5, then we can replace these in the above equation:
Then the linear equation is:
b) Now we want to predict the median salary in 2048. For 2048 the x-value is x = 48
So we just need to evaluate this in the linear equation:
Then the median salary in 2048 will be $2.853 million
If you want to learn more, you can read:
Check the picture below
so.. hmm notice the center h,k and the major and minor axis components, thus just plug them in.
so.. hmm notice the center h,k and the major and minor axis components, thus just plug them in.