Question

How do find the slope and intercept of \[\dfrac{2}{3}x+\dfrac{1}{6}y=2\]?

Answer 1

Hint: From the question we have been asked to find the slope and intercept of an equation. For this question we will use the concept of straight lines. We will use the general form which is known as the slope intercept form of a line that is \[\Rightarrow y=mx+c\] and solve the question further using basic mathematical operations like division, subtraction. So, we proceed with our solution as follows.

Complete step by step solution:
Firstly, as mentioned above the general form of a line with parameters of slope and intercept included, that is the slope intercept form of a line is as follows.
\[\Rightarrow y=mx+c\]
Where m is the slope of the line and c is the intercept of the line.
So, we will try and reduce our given equation in this general form and compare it with the general form of the line and find the required slope and intercept.
We are given,
\[\Rightarrow \dfrac{2}{3}x+\dfrac{1}{6}y=2\]
We will send the \[\dfrac{2}{3}x\] to the other side that is the right hand side of the equation. So, the equation will be reduced as follows.
\[\Rightarrow \dfrac{2}{3}x+\dfrac{1}{6}y=2\]
\[\Rightarrow \dfrac{1}{6}y=2-\dfrac{2}{3}x\]
Now we will multiply with \[6\] on both sides of the equation.
So, the equation will be reduced as follows.
\[\Rightarrow y=-\dfrac{2}{3}\times 6x+2\times 6\]
\[\Rightarrow y=-4x+12\]
So, we compare this with the general form of the line \[y=mx+c\]. So, we get,
The slope as \[-4\] and the intercept as \[12\].

Note: Students must be very careful in doing the calculations. Students should have good concepts in straight lines and its applications. Students should know the formulae of slope intercept form which is \[ y=mx+c\].