What is the slope of the line that passes through the pair of points (3/2,-2) and (-3,7/3)
To find the slope of the line passing through two points, we use the formula
\[m = \frac{y_2-y_1}{x_2-x_1}\]
Let's label the coordinates of the two points:
Point 1: $\left( \frac{3}{2}, -2 \right)$
Point 2: $\left( -3, \frac{7}{3} \right)$
Plugging these values into the formula, we get:
\[m = \frac{\frac{7}{3} - (-2)}{-3-\frac{3}{2}}\]
Simplifying, we have:
\[m = \frac{\frac{7}{3} + \frac{6}{3}}{-\frac{9}{2}}\]
Combining the numerators, we get:
\[m = \frac{\frac{13}{3}}{-\frac{9}{2}}\]
To divide by a fraction, we can multiply by its reciprocal, so:
\[m = \frac{13}{3} \cdot \left( -\frac{2}{9} \right)\]
Multiplying the numerators and denominators separately, we find:
\[m = \frac{13 \cdot (-2)}{3 \cdot 9}\]
Simplifying the numerator and denominator gives us:
\[m = \frac{-26}{27}\]