Question

How do you find the slope given by $y = - 6x + 5$ ?

Answer 1

Hint : To solve this question we should know about linear equations.
Linear equation: The equation having the highest power of its variable is one.
General linear equation in slope intercept form is $y = mx + c$ .
Here, $m$ is slope and $c$ is the y-intercept.

Complete step-by-step answer :
As the given equation is $y = - 6x + 5$ .
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;
$y = \dfrac{C}{B} - \dfrac{A}{B}x$
Comparing it with general slope intercept form that is $y = mx + c$ . we get,
The slope of an equation in standard form is $m = - \dfrac{A}{B}$ .
We can write given equation as;
$\left( 1 \right)y = \left( { - 6} \right)x + 5$
$\left( 6 \right)x + \left( 1 \right)y = 5$
We can get here,
$A = 6,B = 1\,and\,C = 5$
Therefore:
$\bullet$ the slope is: $m = - \dfrac{6}{1} = - 6$
So, the correct answer is “m = -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: $y = mx + c$
If two lines are parallel then the slope of both lines will be equal.
If two lines are perpendicular then the product of slope will be $- 1$ .