if x is partly constant and partly varies with y when y=5,x=19 and when y=10,x=34.
find the relationship between x and y.
find x when y=7
x=a+by
19=a+5b -----(i)
34=a+10b -----(ii)
Multiply equation (i) by 2
38=2a+10b---(iii)
Subtract equation (ii) from (iii)
38=2a+10b
34=a+10b
38-34=2a-a
4=a
:
Well, it seems like x is quite the tricky character, partly constant and partly varying with y. It's like one of those unpredictable clowns at a circus! Let's see if we can unravel this mystery.
First, let's find the change in x when y goes from 5 to 10. We have:
Change in x = x when y=10 - x when y=5
= 34 - 19
= 15
So, the change in x is 15 when y increases by 5. Now, let's find the relationship between x and y.
To find the relationship, we divide the change in x by the change in y:
Relationship = Change in x / Change in y
= 15 / 5
= 3
So, the relationship between x and y is x = 3y. Now, let's find x when y = 7.
x = 3 * 7
= 21
Therefore, when y = 7, x = 21. Voila! The clownish mystery has been solved.
substitute a=4 into equation (i)
19=4+5b
15=5b
b=3
a=4 and b=3
Relationship between x and y is
x=4+3y
When y =7,
x=a+by
x=4+3×7
x=4+21
x=25
To find the relationship between x and y, we need to examine the given data points. From the information provided, we have two sets of values for x and y:
When y = 5, x = 19
When y = 10, x = 34
Let's analyze the change in x as y increases from 5 to 10. We can calculate the difference in x for each step:
Change in x = x(when y = 10) - x(when y = 5)
Change in x = 34 - 19
Change in x = 15
So, as y increases by 5 (from 5 to 10), x increases by 15.
This implies that for every unit increase in y, x increases by 15/5 = 3.
Now we can express the relationship between x and y in terms of a linear function:
x = m * y + b
Where:
m = slope of the line
b = y-intercept
From our calculations, we found that the slope of the line (m) is 3.
Substituting the values of x and y from one of the given data points (e.g., y = 5, x = 19), we can solve for the y-intercept (b):
19 = 3 * 5 + b
19 = 15 + b
b = 19 - 15
b = 4
Therefore, the relationship between x and y is given by: x = 3y + 4.
To find x when y = 7, we can substitute y = 7 into the equation x = 3y + 4:
x = 3 * 7 + 4
x = 21 + 4
x = 25
Thus, when y = 7, x = 25.
I want an answer
Yes
x = a + by
you are given that
19 = a + 5b
34 = a + 10b
So, solve for a and b, and then plug in y=7