Question

Two quantities x and y are such that y is partly constant and partly varies as x . Given that x=3, y=7 and when x=8,y=22.Find the equation connecting x and y

Answer 1

To find the equation connecting x and y, calculate the slope using the given points and then solve for the y-intercept. The derived equation is y = 3x - 2.

Step-by-step explanation:

The student is asking for help finding the equation that connects two quantities, x and y, where y is partly constant and partly varies with x. Given two sets of values for x and y, we can find the equation of the form y = mx + b, where m is the slope (rate of change of y with respect to x) and b is the y-intercept (the constant part of y).

Using the given points (3,7) and (8,22), we can calculate the slope m:

1. m = (y2 - y1) / (x2 - x1) = (22 - 7) / (8 - 3) = 15 / 5 = 3.

Now we can use one of the given points and the slope to find the y-intercept b:

7 = 3(3) + b
b = 7 - 9
b = -2

Thus, the equation connecting x and y is y = 3x - 2.