Question

How do you identify the slope for \[2x - 3y = 12\]?

Answer 1

Hint: Here in this question, we have to identify the slope for the given equation using the slope and the intercept. The slope intercept form of the equation of the line is given as or defined as \[y = mx + c\], where m represents the slope of the given equation. By rearranging the terms in the form of slope intercept form we identify the slope.

Complete step by step solution:
The given equation should be written in the form of \[y = mx + b\], where m is slope and b is known as y-intercept. Slope means ratio of vertical change to the horizontal change i.e., ratio of change in y-axis or step size of y-axis to the change in x-axis or step size of x-axis. An intercept is a point where the straight line or a curve intersects the y-axis in a plane. If the point x is zero then the obtained point is a y -intercept.
Now consider the given equation in the given question.
\[2x - 3y = 12\]
Usually these equations will represent the equation of the line and this equation is in the linear form.
Here in this question we have found the slope of the equation. So first we write the given equation in the form of \[y = mx + c\].
Therefore now take 12 to LHS and -3y to the RHS and we get.
\[ \Rightarrow 2x - 12 = 3y\]
and this can be written as
\[ \Rightarrow 3y = 2x - 12\]
Now we will divide the equation by 3 and we get
\[ \Rightarrow y = \dfrac{2}{3}x - \dfrac{{12}}{3}\]
On simplifying we get
\[ \Rightarrow y = \dfrac{2}{3}x - 4\]
When we compare the above equation to the slope intercept equation, the slope of the equation \[2x - 3y = 12\] is \[\dfrac{2}{3}\]
Hence we have identified the slope of the given equation.
So, the correct answer is “\[\dfrac{2}{3}\]”.

Note: Here to find the slope first we have to know the slope intercept form and which is given as \[y = mx + b\], and further we have shift the terms and we have to make the given equation to the slope intercept form and while shifting the terms we must be aware of the signs because while shifting the sign will change.