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Question: How do you find the slope given \( - 2x - 7y = 21\) ?...

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

Explanation

Solution

The equation of a straight line in slope-intercept form is: y=mx+by = 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
⇒−2x−7y=21\Rightarrow - 2x - 7y = 21
Let us add 2x on both sides.
⇒−2x+2x−7y=21+2x\Rightarrow - 2x + 2x - 7y = 21 + 2x
Therefore,
⇒−7y=21+2x\Rightarrow - 7y = 21 + 2x
Now, let us divide both sides by -7.
⇒y=21+2x−7\Rightarrow y = \dfrac{{21 + 2x}}{{ - 7}}
Now, simplify the above equation in standard form.
⇒y=−2x−217\Rightarrow y = \dfrac{{ - 2x - 21}}{7}
Let us split the denominator.
⇒y=−2x7−217\Rightarrow y = - \dfrac{{2x}}{7} - \dfrac{{21}}{7}
Hence,
⇒y=−27x−3\Rightarrow y = - \dfrac{2}{7}x - 3
Now, compare the above equation with a straight line equationy=mx+cy = mx + c
So, we get m=−27m = - \dfrac{2}{7} and c=−3c = - 3

Hence, the value of slope is −27 - \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(m)=y2−y1x2−x1slope\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.