Use substitution to solve the system of equations.
1 answer:
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Answer:
- Inverse Variation
- Equation:
Step-by-step explanation:
Given
X-> 2 | 4 | 8 | 12
Y-> 6 | 3 | 3/2 | 1
Required
- State the type of variation the table represents
- Determine the equation to model the data
To check for type of variation; we'll make use of trial by error method.
To start with; We'll check for direct variation.
This is done using the following expression;
where k is the constant of variation
Make k the subject of formula
When Y = 6, X= 2
When Y = 3, X = 4
There's no need to check further as both values of k are not equal
To check for inverse variation;
Make k the subject of formula
When Y = 6, X= 2
When Y = 3, X = 4
When Y = 3/2; X = 8
When Y = 1, X = 12
Note that for all values of X and Y, K remains constant;
Hence, the table represents an inverse direction
To determine the equation;
We make use of
Substitute 12 for k
So, the equation becomes
Reorder
Hence, the equation is
First you have to get the equation into slope/intercept format: y = mx + b
So the slope m = 2, and the y-intercept b = -1.
b tells you where the line intersects the y axis. The slope is rise (vertical distance) over run (horizontal distance). I have attached my best attempt at drawing this without graph paper. The dotted line represents the inequality, and the solution set includes the values above the line which is why it is shaded. Hope this helps!
