Help would be greatly appreciated!!! This gets really confusing for me.
Write an inverse variation equation. If y varies inversely with x and y=2 when x=4….
a. Find K.
b. Write a general equation.
c. Use your equation to find y when x=8
Draw a chart to show at least 5 ordered pairs that are on the graph. (Hint: don’t pick all positive numbers)
x- y-
Since you know about k, you must surely have grasped the idea that if y varies directly with x, then
y = kx
You know that y=2 when x=4, so
2 = k*4
k=1/2
... the rest should be easy. Just use your fancy new equation.
y = x/2
8/2 = 4, so y=4 when x=8
x: -21 -3.4 0 π 6
y: -21/2 -1.7 0 π/2 3
a. Well, finding K is as simple as dividing y by x in this case. So, if y = 2 when x = 4, we can calculate K by dividing y by x: 2/4 = K. And what's 2 divided by 4? Hmmm... That's a tricky one, let me think... Ah, it's 0.5!
b. Alright, alright, let's write a general equation. Inverse variation equations take the form y = K/x, where K is that fancy constant we just found. So, our general equation would be y = 0.5/x. You got this!
c. Time to put our equation from part b to use. We want to find y when x is 8. Remember, we have y = 0.5/x. Plug in x = 8, and voila! y = 0.5/8. Now, the suspense is killing me... let's simplify that: y = 0.0625. Just like that, we've got our y value!
Now, for the chart. We need 5 ordered pairs, so let's get this party started:
x- y-
1 0.5
2 0.25
3 0.16666666666666666666666666666667 (phew, that's a mouthful! I hope you have enough space on your chart!)
-1 -0.5
-4 -0.125
There we have it! Five intriguing ordered pairs for your chart. Have fun with those!
a. To find the constant of variation, K, we can use the given values of y and x. Since y varies inversely with x, we can set up the equation: y = K/x.
Given that y = 2 when x = 4, we can substitute these values into the equation: 2 = K/4.
To find K, we can cross multiply: 2 * 4 = K.
Simplifying, we get: 8 = K.
Therefore, K equals 8.
b. Now that we have found K, we can write the general equation in inverse variation form: y = 8/x.
c. To find y when x = 8, we can substitute the value of x into the general equation: y = 8/8.
Simplifying, we get: y = 1.
Therefore, when x = 8, y = 1.
To draw a chart showing ordered pairs, we can choose x-values and calculate the corresponding y-values using the equation y = 8/x.
Let's choose the following x-values: -2, -1, 0, 1, and 2.
- When x = -2, y = 8/-2 = -4.
- When x = -1, y = 8/-1 = -8.
- When x = 0, y is undefined because division by zero is undefined.
- When x = 1, y = 8/1 = 8.
- When x = 2, y = 8/2 = 4.
The table of ordered pairs is as follows:
x | y
-2 | -4
-1 | -8
0 | undefined
1 | 8
2 | 4
These ordered pairs represent points on the graph of the inverse variation equation.
Sure! I can help you with that. Inverse variation is a relationship between two variables where their product is a constant. Mathematically, it can be represented as:
y = k/x
where k is the constant of variation.
a. To find the value of k, we can substitute the given values into the equation: y = k/x. We know that y = 2 when x = 4. Let's plug these values into the equation:
2 = k/4
To find the value of k, we can multiply both sides of the equation by 4:
2 * 4 = k
8 = k
Therefore, the value of k is 8.
b. Now that we have the value of k, we can write the general equation for this inverse variation as:
y = 8/x
c. To find y when x = 8, we can substitute it into the equation:
y = 8/8
y = 1
Therefore, when x = 8, y = 1.
d. Let's create a chart with at least 5 ordered pairs. Since we want to avoid using all positive numbers, let's select values with different signs for x and y. Here's an example:
x y
1 -8
2 -4
4 2
-2 4
-4 8
These are five ordered pairs that satisfy the inverse variation equation y = 8/x.