Question

The ordered pair $(2,10)$, is a solution of a direct variation, how do you write the
equation of a direct variation, then graph your equation and show that the slope of the line is equal to the constant of variation?

Answer 1

We will start off by setting up proportions, for boys and girls. We will consider an unknown variable as $x$ to further simplify and evaluate the terms. Then cross multiply terms and evaluate the number of boys in the school.

Complete step by step answer:
We will start off by forming a relation between the variables $x,y$.
So, according to the given conditions, $y\,\alpha \,x$.
Now if we consider any variable as a constant of variation, we can write the above equation as,
$y = kx$ where $k$ is the constant of variation.
Now, here we will evaluate the value of $k$ with the help of given coordinates which are $(2,10)$.
$y = kx \\\ k = \dfrac{y}{x} \\\ k = \dfrac{{10}}{2} \\\ k = 5 \\\$
Now substitute the value of $k$ in the equation.
$y = 5x$
So, the equation of line is in the slope point form which is given by $y = mx + c$ where $m$ is slope and $c$ is the y-intercept. As we can see, the slope of our line is $5$ and the y-intercept is $0$.

Note: While converting orders do not matter for addition and multiplication. But order is important for subtraction and division. Make sure that you read the statement twice before translating it to an expression. Pay extra attention to the statements where multiplication and division is involved. While cross multiplying the terms, make sure to multiply the terms along with their signs.