To compare the slopes between the pairs of points, we can use the formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
First, let's calculate the slope between the points (4, 30) and (12, 90):
Here, \((x_1, y_1) = (4, 30)\) and \((x_2, y_2) = (12, 90)\).
\[ m = \frac{90 - 30}{12 - 4} = \frac{60}{8} = 7.5 \]
Next, let's calculate the slope between the points (4, 30) and (10, 75):
Here, \((x_1, y_1) = (4, 30)\) and \((x_2, y_2) = (10, 75)\).
\[ m = \frac{75 - 30}{10 - 4} = \frac{45}{6} = 7.5 \]
Conclusion:
Both calculations yield the same slope of 7.5. This means that the slope between (4, 30) and (12, 90) is the same as the slope between (4, 30) and (10, 75).
Thus, the correct comparison is:
The slope between (4, 30) and (12, 90) and between (4, 30) and (10, 75) is the same.