Question

How do you find the slope of $ x - y = 5 $ ?

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 x - y = 5 $
Let us subtract x on both sides.
 $ \Rightarrow x - x - y = 5 - x $
Therefore,
 $ \Rightarrow - y = 5 - x $
Now, let us multiply both sides by -1.
 $ \Rightarrow \left( { - 1} \right)\left( { - y} \right) = \left( { - 1} \right)\left( {5 - x} \right) $
Now, simplify the above equation.
 $ \Rightarrow y = - 5 + x $
Let us rewrite the above equation.
 $ \Rightarrow y = x - 5 $
Now, compare the above equation with a straight line equation $ y = mx + b $
So, we get $ m = 1 $ and $ b = - 5 $

Hence, the value of the slope is 1.

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.