find the slope of the line containing the following points:
(5/6 , -5) (-1/3, -1/3)
can someone please help me I keep getting different answers.. I am not good at fractions especially with the negative signs... thanks
slope = (-1/3 - (-5))/(-1/3 - 5/6)
= (-1/3 + 5)/(-1/3 - 5/6)
here is a cool trick:
multiply top and bottom by 6, the LCD
m = (-2 + 30)/(-2 - 5)
= 28/-7
= -4
To find the slope of a line containing two points, you can use the slope formula:
m = (y2 - y1) / (x2 - x1)
Let's assign the coordinates of the first point as (x1, y1) and the coordinates of the second point as (x2, y2). In this case, we have:
Point 1: (x1, y1) = (5/6, -5)
Point 2: (x2, y2) = (-1/3, -1/3)
Now, substitute these values into the slope formula:
m = (-1/3 - (-5)) / (-1/3 - 5/6)
First, simplify the numerator:
y2 - y1 = -1/3 - (-5) = -1/3 + 5 = 5 - 1/3
To add these mixed numbers, find a common denominator:
5 = 5/1 and 1 = 1/1
Now, the denominator:
x2 - x1 = -1/3 - 5/6
To subtract fractions with different denominators, find a common denominator:
The LCM (Least Common Multiple) of 3 and 6 is 6.
-1/3 = -2/6 (multiply the numerator and denominator by 2)
5/6 remains the same
Now, we can continue simplifying the denominator:
-2/6 - 5/6 = -7/6
Putting it all together:
m = (5 - 1/3) / (-7/6)
Next, we can simplify the expression in the denominator:
-7/6 = -(7/6)
This is equivalent to (-1)*(7/6) = -7/6
Now, the slope can be simplified as follows:
m = (5 - 1/3) / (-7/6)
= (15/3 - 1/3) / (-7/6)
= (14/3) / (-7/6)
= (14/3) * (-6/7)
= -84/21
Simplify the fraction:
-84/21 = -4
So, the slope of the line containing the given points is -4.