what is the slope of the line that passes through the pair of points (1/2, -4), (-2/3, 5)
To find the slope of a line passing through two points (x₁, y₁) and (x₂, y₂), we can use the slope formula:
slope = (y₂ - y₁) / (x₂ - x₁)
In this case, the points are (1/2, -4) and (-2/3, 5), so we have:
x₁ = 1/2
y₁ = -4
x₂ = -2/3
y₂ = 5
Using the slope formula:
slope = (5 - (-4)) / (-2/3 - 1/2)
= 9 / (-2/3 - 1/2)
= 9 / (-4/6 - 3/6)
= 9 / (-7/6)
= 9 * (-6/7)
= -54/7
Therefore, the slope of the line passing through the points (1/2, -4) and (-2/3, 5) is -54/7.