Question

How do you convert find the slope of 3x-6y = 12?

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 $3x-6y=12$ , 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 $y=\dfrac{1}{2}x-2$. So, we will say that the line $y=\dfrac{1}{2}x-2$ has slope equal to $\dfrac{1}{2}$ and y-intercept equal to -2.

Complete step by step answer:
We know that the above question is a linear equation in one variable.
We also know that 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 compare the given equation with y = mx + c.
The given equation of line is 3x-6y = 12.
Now, we will divide both the LHS and RHS of the given equation with 6 so that the coefficient of y can be made 1.

& \Rightarrow \dfrac{3x-6y}{6}=\dfrac{12}{6} \\\ & \Rightarrow \dfrac{3x}{6}-\dfrac{6y}{6}=2 \\\ & \Rightarrow \dfrac{1}{2}x-y=2 \\\ \end{aligned}$$ Now, we will take x terms towards the RHS: $\Rightarrow -y=-\dfrac{1}{2}x+2$ Now, after multiplying both side by minus(-) we will get: $\Rightarrow y=\dfrac{1}{2}x-2$ Now, we will compare the equation $y=\dfrac{1}{2}x-2$ with the general equation y = mx + c. After comparing we will get: $m=\dfrac{1}{2}$ and $c=-2$ . So, the slope of the line 3x-6y = 12 is equal to $\dfrac{1}{2}$, 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.