Question

Find the slope of a line whose equation is given by \[3x + 5y = - 2\].

Answer 1

Hint: To find the slope of the given line for the given question, we will first transform the equation of the line into the standard form of the line which is \[y = mx + c\]where the value of m is equal to the slope of the line. After transforming the equation we will compare the equation with the standard to determine slope.

Complete step by step solution:
Before dwelling on the question let us first understand what is the slope of an equation and how it is determined. Simply put, if theta is the inclination of any line L then tanθ is called the slope or gradient of the line L. The slope of a line is determined by m. Thus, m= tanθ, θ is not equal to 90°. It is important to note here that the slope of the x-axis is zero and the slope of the y-axis is not defined.

Consequently, the slope of any line L with vertices \[\left( {{x_1},{y_1}} \right)\left( {{x_2},{y_2}} \right)\]is given by
\[ \Rightarrow m = \dfrac{{{y_2} - {y_1}}}{{{x_{2 - }}{x_1}}}\]
Now based on our understanding of slopes, we will try and solve our given question,
Given the equation of the line is,\[3x + 5y = - 2\]
\[ \Rightarrow 5y = - 3x - 2\]
\[ \Rightarrow y = - \dfrac{3}{5}x - 2 - - - - - \left( 1 \right)\]
We know that the standard form of the equation of a line is given by \[y = mx + c\], where m is the slope of the line. Now, comparing the equation (1) with the standard form of the equation we get, \[ \Rightarrow m = - \dfrac{3}{5}\] which is the required slope of the line.

Hence the correct answer is \[m = - \dfrac{3}{5}\].

Note: One of the important things to note here is that in \[y = mx + c\], two constants are mand c. the value of c can be negative as well as positive as the intercept can be made at the negative or positive side of the y-axis.