Question

How do you find the slope for $2x + 3y = 12$?

Answer 1

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$- \dfrac{2}{3}$.