Question

How do you write the equation in slope intercept form given x – 3y = 6?

Answer 1

The above given question is of linear equation in one variable. Since, we know that the slope intercept form of the line equation is given as y = mx + c, where m is the slope of the line and c is the y-intercept. In the given equation $x-3y=6$ , we will first make the coefficient of the y as 1 and then take the ‘x’ terms to the RHS. The equation which we will get is $y=\dfrac{1}{3}x-2$. So, we will say that the line $y=\dfrac{1}{3}x-2$ has slope equal to $\dfrac{1}{3}$ and y-intercept equal to -2.

Complete step-by-step solution:
We know that the above question is a linear equation in one variable.
We also know that the slope-intercept form of the linear equation is given by y = mx + c, where m is the slope of the line and c is the y-intercept. Slope is the tangent of the angle made by the line with x-axis and y-intercept is the point at which the line cuts the y-axis.
Now, we will first make the coefficient of y as 1 and take the x terms to the right of the given equation so that we can easily convert the given equation in y = mx + c form.
The given equation of line is $x-3y=6$.
Now, we will divide both the LHS and RHS of the given equation with 3 so that the coefficient of y can be made 1.

& \Rightarrow \dfrac{x-3y}{3}=\dfrac{6}{3} \\\ & \Rightarrow \dfrac{x}{3}-y=2 \\\ & \Rightarrow \dfrac{1}{3}x-y=2 \\\ \end{aligned}$$ Now, we will take x terms towards the RHS: $\Rightarrow -y=-\dfrac{1}{3}x+2$ Now, after multiplying both side by minus(-) we will get: $\Rightarrow y=\dfrac{1}{3}x-2$ Now, we can see that the above equation is in standard form of slope-intercept form of the line i.e. y = mx + c. So, the slope of the line $y=\dfrac{1}{3}x-2$ is equal to $\dfrac{1}{3}$, and the y-intercept is equal to -2. We can plot the graph of the line as:  This is our required solution. **Note:** Student are required to note that when we have general equation of the line as $ax+by+c=0$ , then slope of the line is equal to $-\dfrac{a}{b}$ and y-intercept is equal to $-\dfrac{c}{a}$ . We can also find the slope of the line by equating the first derivative of the line equation to 0 i.e. $\dfrac{dy}{dx}=0$ and when we put x = 0, we will get the y-intercept of the line. And, then we will put the value of slope and y-intercept of the line in the general equation of the slope-intercept form y = mx + c, where m is the slope of the line equation and c is the y-intercept.