Question

How do you find the slope and intercept of $x - y = 1$ ?

Answer 1

Hint: To solve this question we should know about linear equations. Linear equation in two variables: The equation having the highest degree on any variable. Be should keep in mind always LHS is equal to RHS if not then we are doing the wrong solution.

Complete step by step solution:
As the given equation is $x - y = 1$ .
This equation is in standard linear form and the standard form of a linear equation is:
 $Ax + By = C$
Where, if at all possible, $A$ ,$B$ , and $C$ are integers, and A is non-negative, and A, B, and C have no common factors other than $1$
So, we can change it into;
\[\Rightarrow y = \dfrac{C}{B} - \dfrac{A}{B}x\]
Comparing it with general slope intercept form that is $y = mx + c$ . we get,
The slope of an equation in standard form is $m = - \dfrac{A}{B}$ .
And,
The y-intercept of an equation in standard form is $\dfrac{C}{B}$ .
We can write given equation as;
$\Rightarrow 1x + \left( { - 1} \right)y = 1$
We can get here,
$\Rightarrow A = 1,B = - 1\,and\,C = 1$
Therefore:
$ \Rightarrow $ the slope is: $m = \dfrac{{ - 1}}{{ - 1}} = 1$
$ \Rightarrow$ the $y$ -intercept is: $\dfrac{1}{{ - 1}} = - 1\,or(0, - 1)$

Note: There are many general form of linear equation:
General form: $Ax + By + C = 0$
Point-slope form: $y - {y_1} = m(x - {x_1})$
Slope intercept form: $y = mx + c$