Question

Find the slope of $3x + 2y = - 6$.

Answer 1

In the given problem, we are required to find the slope of a line whose equation is given to us. We can easily tell the slope of a line written in slope intercept form. So, we first have to write the line in slope intercept form and then find the slope of the straight line given. For converting the line to slope intercept form, we need to have knowledge of algebraic methods like transposition rule.

Complete step by step answer:
We are required to find the slope of the straight line $3x + 2y = - 6$ .

Writing in standard form of equation of a straight line $ax + by + c = 0$ , we get,

$3x + 2y + 6 = 0$

Now shifting all terms except terms of y on other side, we get,

$2y = - 3x - 6$

Finding the value of y by taking 2 to other side, we get,

$=$ $y = \dfrac{{ - 3x - 6}}{2}$

$=$ $y = \left( {\dfrac{{ - 3x}}{2}} \right) + \left( {\dfrac{{ - 6}}{2}} \right)$

Further simplifying the equation and doing the calculations, we get,

$=$ $y = \left( {\dfrac{{ - 3x}}{2}} \right) + ( - 3)$

On comparing with slope intercept form of straight line $y = mx + c$, where slope is given by ‘m’

Thus the slope of straight line $3x + 2y = - 6$ is $\left( { - \dfrac{3}{2}} \right)$ .

Note: The given problem can be solved by various methods. We can find the slope of a line by expressing it in point and slope form as well as slope and intercept form. We can also apply a direct formula for calculating the slope of a line: Slope of line$= - \left( {\dfrac{{{\text{Coefficient of x}}}}{{{\text{Coefficient of y}}}}} \right)$ when the equation of straight line is written in standard form $ax + by + c = 0$ .