Question

How do you find the slope given \[y = - \dfrac{1}{2}x + 4\]?

Answer 1

Hint: Rewrite the given line equation to standard line equation \[y = mx + c\] and then compare the terms to find the slope of the given equation, where m is the slope.

Complete step by step solution:
Given the line equation,
\[y = - \dfrac{1}{2}x + 4\]
On rewriting the above equation to the standard from of line equation which is \[y = mx + c\]
Where m is slope here and c is constant
Since the given line equation is in the standard form, we can compare directly.
 \[y = - \dfrac{1}{2}x + 4\]
Now on comparing the above line equation with the standard one we will get
\[y = mx + c\]
Here\[m = - \dfrac{1}{2},c = 4\].

Therefore the slope of the given equation is\[m = - \dfrac{1}{2}\].

Additional information: If you are provided with the line equation, then it is not a big deal to find the slope you can easily find the slope, but when you are provided with two points to find the slope then you have to use the formula
Slope \[ = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\]
Even if you can find the point on the line by substituting \[x = 0\] you will get the first point and substitute \[y = 0\] for the second point and use the above formula.

Note: Slope can be either positive or negative, it doesn’t mean you solved correctly if you get positive slope or negative slope, all you need to do is to make the given line equation into standard format and then compare the values to get the slope of a line.