Question

What is the slope and y intercept of $6x-3y=12$ ?

Answer 1

Hint: To find the slope and y intercept of $6x-3y=12$ , we have to convert this equation into its slope-intercept form by rearranging and simplifying the equation. The slope-intercept form is given by $y=mx+c$ , where, m is the slope and c is the y-intercept.

Complete step-by-step answer:
We have to find the slope and y intercept of $6x-3y=12$ . Let us convert the given equation into slope-intercept form which is given by $y=mx+c$ , where, m is the slope and c is the y-intercept.
Now, let us consider the given equation. We have to move 6x to the RHS.
$\begin{align}
  & \Rightarrow 6x-3y=12 \\
 & \Rightarrow -3y=12-6x \\
\end{align}$
Now, we have to move the coefficient of y to the RHS.
$\Rightarrow y=\dfrac{12-6x}{-3}$
Let us rewrite the RHS as follows.
$\Rightarrow y=\dfrac{12}{-3}-\dfrac{6x}{-3}$
Now, we have to cancel the common factor 3 from the RHS.
$\Rightarrow y=-4+2x$
Let us rearrange the above equation.
$\Rightarrow y=2x-4$
Now, the above equation is in the slope-intercept form. We can see that the slope is, $m=2$ and y-intercept is -4.
Hence, the slope and y intercept of $6x-3y=12$ is 2 and -4 respectively.

Note: Students must know the slope-intercept form thoroughly. They have a chance of making mistakes by writing the slope-intercept form as $x=my+c$ . y-intecept is obtained when the value of x is zero in the slope-intercept form. Similarly, we can find the x-intercept by substituting the value of y as zero. Students must know the algebraic rules to simplify the equations.