y is partly constant and partly varies as x,when y=-2,x=5 and when y=-1,x=4,find y when x=3 and x when y=1
the slope of the line is ... (-2 - -1) / (5 - 4)
... y = -1 x + b
plug in one of the given points to find b (the y-intercept ... the constant part)
use the equation to find the missing y and x
(4, -1), (5, -2), (3, y), (x, 1).
m = (-2+1)/(5-4) = -1.
-1 = (y+1)/(3-4).
Y = 0.
-1 = (1+1)/(x-4)
X =
To find the relationship between y and x, we can start by finding the constant part and the varying part separately.
When y is partly constant and partly varies as x, we can express it as:
y = kx + c
where k represents the coefficient of the varying part and c is the constant part.
Now, let's substitute the given values for x and y in the equation to find the values of k and c.
When y = -2 and x = 5:
-2 = 5k + c ........ equation 1
When y = -1 and x = 4:
-1 = 4k + c ........ equation 2
We have two equations with two unknowns (k and c). We can solve these equations simultaneously to find the values of k and c.
Subtracting equation 2 from equation 1, we get:
-2 - (-1) = 5k - 4k + c - c
-1 = k
Now, substituting the value of k = -1 into equation 1, we get:
-2 = 5(-1) + c
-2 = -5 + c
c = -2 + 5
c = 3
So, we have found the values of k and c.
Now, we can substitute these values into the equation y = kx + c to find the values of y when x = 3 and x when y = 1.
For x = 3:
y = (-1)(3) + 3
y = -3 + 3
y = 0
When x = 3, y = 0.
For y = 1:
1 = (-1)x + 3
1 - 3 = -x
-2 = -x
x = 2
When y = 1, x = 2.
To find the relationship between y and x, we can use the given information to create an equation.
Let's start by finding the part of y that is constant. When y = -2 and x = 5, we know that y + kx = -2, where k is the constant of proportionality. Plugging in the values, we have -2 + 5k = -2.
Simplifying the equation, we get 5k = 0, and dividing both sides by 5, we find k = 0.
Now, let's find the part of y that varies with x. When y = -1 and x = 4, we have y + kx = -1. Substituting in the value of k we just found, we get y + 0x = -1, which simplifies to y = -1.
So, we have determined that the relationship between y and x is y = -1.
Now, to find y when x = 3, we can substitute x = 3 into the equation y = -1. Therefore, y = -1.
To find x when y = 1, we can substitute y = 1 into the equation y = -1. Therefore, x does not exist for this value of y.
So, y = -1 when x = 3, and there is no x when y = 1.