Question

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

Answer 1

Hint: Here, we have to find the slope of the given equation of the line. We will compare the given equation of the line with the standard equation of a line to find the coefficients of the variables and the constant term. Then using these and the slope formula, we will find the required slope of the line.

Formula used:
Slope of the equation of line is given by the formula \[m = - \dfrac{a}{b}\]

Complete step by step solution:
We are given an equation of line \[2x + 3y = 12\].
The standard equation of line is of the form \[ax + by = c\].
Comparing the given equation of line with the standard equation of line, we get \[a = 2;b = 3;c = 12;\]
Now, we will find the slope for the equation of line \[2x + 3y = 12\].
Slope of the equation of line is given by the formula \[m = - \dfrac{a}{b}\]
By substituting the values of \[a = 2\] and \[b = 3\] in the formula, we get
\[m = - \dfrac{2}{3}\]

Therefore, the slope of the equation of line \[2x + 3y = 12\] is \[ - \dfrac{2}{3}\].

Additional Information:
We know that slope is defined as the ratio of change in the y axis to the change in the \[x\] axis. A slope can be represented in the parametric form and in the point form. A point crossing the \[x\]-axis is called \[x\]-intercept and A point crossing the y-axis is called the y-intercept. The slope of a line is used to calculate the steepness of a line. We know that the Slope of a line is used to find the equation of a line.

Note:
We can also find the slope using the slope- intercept form. Slope- Intercept Form of the equation of line is \[y = mx + c\] where \[m\] is the slope and \[c\] is the \[y\]-intercept. Thus, the given equation is written in the slope- intercept form, we get
\[ 2x + 3y = 12\]
By rewriting the given equation in the slope-intercept form, we get
\[ \Rightarrow 3y = - 2x + 12\]
\[ \Rightarrow y = \dfrac{{ - 2}}{3}x + \dfrac{{12}}{3}\]
By simplifying the equation, we get
\[ \Rightarrow y = \dfrac{{ - 2}}{3}x + 4\]
By comparing with equation of line in slope-intercept form, we get\[m = - \dfrac{2}{3}\] and\[c = 4\]
Therefore, the slope of the equation of line\[2x + 3y = 12\]is\[ - \dfrac{2}{3}\].