X is partly constant and partly varies with y. When y = 5, x = 19 and when y=10, x = 35. Find the relationship between x and y
To find the relationship between x and y, we need to determine how x changes as y changes. Let's first identify the constant part of x.
When y = 5, x = 19. This gives us one data point: (5, 19).
Now, let's determine the difference in x between the two given data points:
Δx = x₂ - x₁ = 35 - 19 = 16
Next, let's find the difference in y between the two data points:
Δy = y₂ - y₁ = 10 - 5 = 5
Since x is partly constant and partly varies with y, we need to determine the relationship between x and y for the varying part.
To find the varying part of x, we divide the difference in x by the difference in y:
m = Δx / Δy = 16 / 5 = 3.2
So, we have determined the value of the slope, which is equal to 3.2.
Let's write the equation of the relationship between x and y using the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.
Since x is partly constant, we can determine the value of b using the first data point (5, 19):
19 = 3.2 * 5 + b
19 = 16 + b
b = 19 - 16
b = 3
Now we can write the equation:
y = 3.2x + 3
Therefore, the relationship between x and y is given by the equation y = 3.2x + 3.