6. What is the slope of the line that passes through the pair of points ((1/2), -4) and (-2/3, 5)?
Show your work below.
To find the slope of the line passing through the points ((1/2), -4) and (-2/3, 5), we can use the slope formula:
m = (y2 - y1) / (x2 - x1)
Let's assign the coordinates of the first point to (x1, y1) and the coordinates of the second point to (x2, y2):
x1 = 1/2, y1 = -4
x2 = -2/3, y2 = 5
Substituting these values into the slope formula, we get:
m = (5 - (-4)) / (-2/3 - 1/2)
Simplifying the expression inside the parentheses:
m = 9 / (-2/3 - 1/2)
To subtract fractions, we need a common denominator:
m = 9 / (-4/6 - 3/6)
Combine the fractions with common denominators:
m = 9 / (-7/6)
Dividing by a fraction is equivalent to multiplying by its reciprocal:
m = 9 * (-6/7)
Simplifying the expression:
m = -54/7
The slope of the line passing through the points ((1/2), -4) and (-2/3, 5) is -54/7.