Question

How do you find the slope given $ - 2x - 7y = 21$ ?

Answer 1

Hint: The equation of a straight line in slope-intercept form is: $y = mx + b$. Where m is the value of slope and b is the y-intercept. Here, m and b are constants, and x and y are variables. Since x and y are variables that describe the position of specific points on the graph, m and b describe features of the function. A straight line is a linear equation of the first order. In this question, a linear equation is given. We will convert this equation into the form of a straight-line equation. By comparing with the standard equation we will find the value of slope and the value of intercept.

Complete step by step solution:
In this question, the linear equation is
$ \Rightarrow - 2x - 7y = 21$
Let us add 2x on both sides.
$ \Rightarrow - 2x + 2x - 7y = 21 + 2x$
Therefore,
$ \Rightarrow - 7y = 21 + 2x$
Now, let us divide both sides by -7.
$ \Rightarrow y = \dfrac{{21 + 2x}}{{ - 7}}$
Now, simplify the above equation in standard form.
$ \Rightarrow y = \dfrac{{ - 2x - 21}}{7}$
Let us split the denominator.
$ \Rightarrow y = - \dfrac{{2x}}{7} - \dfrac{{21}}{7}$
Hence,
$ \Rightarrow y = - \dfrac{2}{7}x - 3$
Now, compare the above equation with a straight line equation$y = mx + c$
So, we get $m = - \dfrac{2}{7}$ and $c = - 3$

Hence, the value of slope is $ - \dfrac{2}{7}$ and the value of intercept is -3.

Note:
Slope: The slope of a line is the ratio of change in y over the change in x between any two points on the line.
$slope\left( m \right) = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$
Positive slope: It means that two variables are positively related; that is, when x increases, so do y, and when x decreases, y decreases also. The line with the positive slope on the line graph moves from left to right and the line rises.
Negative slope: A negative slope means that two variables are negatively related; that is, when x increases, y decreases, and when x decreases, y increases. The line with the negative slope on the line graph moves from left to right and the line falls.
The slope is a horizontal line then the value of y is always the same.
The slope is a vertical line then the value of x is always the same.