Question

For the data in the table, does y vary directly with x? If it does write an equation for the direct variation. x 2 6 10 y 5 15 25

Answer 1

The data does show direct variation (otherwise known as direct proportionality);
2 + 4 = 6 5 + 10 = 5
6 + 4 = 10 15 + 10 = 25
The proof is that everytime we increase x by a number (in this case 4), y also increases by some number (in this case 10);
So increasing x by 4, we increase y by 10;
The equation of data that shows direct proportionality is that of a line;
The gradient (represented by m) of the line is going to be how much y changes when we change x;
Using the information above, we can deduce the gradient (m) like so:
m = +10/+4
= 5/2
Now, we use the formula for the equation of the line:
y - y₁ = m(x - x₁)
y - 5 = 5/2(x - 2)
2(y - 5) = 5(x - 2)
2y - 10 = 5x - 10
2y = 5x
y = 5x/2