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 $ .