Question

How do you write $y = \dfrac{2}{3}x$ in standard form?

Answer 1

Hint: We are given an equation in slope-intercept form. Now, we have to find the standard form of the equation. First, we will apply the basic arithmetic operations to both sides of the equation. Then, rewrite the equation in the standard form.

Complete step by step solution:
We are given the equation in slope intercept form.

Now, we will subtract y from both sides.

$ \Rightarrow y - y = \dfrac{2}{3}x - y$

On simplifying the expression, we get:

$ \Rightarrow 0 = \dfrac{2}{3}x - y$

Now, we will multiply both by 3.

$ \Rightarrow 0 \times 3 = 3\left( {\dfrac{2}{3}x - y} \right)$

On simplifying the expression, we get:

$ \Rightarrow 0 = 3 \times \dfrac{2}{3}x - 3y$

$ \Rightarrow 0 = 2x - 3y$

Hence, the equation in standard form is $2x - 3y = 0$.

Note: The equation of the straight line in two variables can be written in slope-intercept form as $y = mx + b$ where $m$ is the slope of the line and $b$is the y-intercept. The y-intercept is the value at which the x-coordinate is equal to zero. The value of the slope is equal to the change in y-coordinate to change in x-coordinate. The linear equation in two variables can be written in two variables as $Ax + By = C$. Similarly, the value x-coordinate is determined by setting $y = 0$ in the equation. The equation of the line will pass through the point $\left( {x,y} \right)$.
The students must note that we basically first rewrite the equation given in slope-intercept form into standard form $Ax + By = C$ by rearranging the terms in the equation where A and B are coefficients of variable x and C is the constant value. From this we can conclude that $A = 2$, $B = - 3$ and $C = 0$