Question

What is the slope of the line \[4x-3y=9\]?

Answer 1

Hint: We are given an equation in two variables, ‘x’ and ‘y’. We will first write the given equation in slope intercept form which is, \[y=mx+c\]. Here, ‘m’ refers to the slope of the given line and ‘c’ is the y – intercept. So, when we write the given equation in the slope intercept form, we get, \[y=\dfrac{4}{3}x-3\]. In comparison, we will get the slope of the given line. Hence, we will have the required value.

Complete step-by-step answer:
According to the given question, we are given the equation of a line and we are asked to find the slope of the given equation of a line.
In order to find the value of slope, we can use the slope intercept form, which is, \[y=mx+c\]. Here, ‘m’ refers to the slope of the given equation of a line and ‘c’ stands for the y – intercept value.
The given equation we have is,
\[4x-3y=9\]----(1)
We will rearrange this equation so that it is in the slope intercept form. We will first subtract 4x from both the sides, we get,
\[\Rightarrow 4x-3y-4x=9-4x\]
We get the expression on solving as,
\[\Rightarrow -3y=9-4x\]
Now, we will divide the above expression by -3 and we get,
\[\Rightarrow \dfrac{-3y}{-3}=\dfrac{9}{-3}-\dfrac{4x}{-3}\]
The new expression that we get is,
\[\Rightarrow y=-3+\dfrac{4}{3}x\]
The slope intercept form of the given equation, we have,
\[\Rightarrow y=\dfrac{4}{3}x-3\]
On comparison with the equation of slope intercept form, we get the value of slope as,
\[m=\dfrac{4}{3}\]
Therefore, the slope of the given equation is \[\dfrac{4}{3}\].

Note: The value of the slope for the given equation can also be obtained graphically. And the equation of the slope which then will be used is, \[m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\], where \[({{x}_{1}},{{y}_{1}})\] and \[({{x}_{2}},{{y}_{2}})\] are the two points on the given equation of line.