Question

this expression shows point bs y - value minus point as y - value in the numerator, and point as x - value minus point bs x - value in the denominator. when you subtracted in the numerator and denominator, you got $-\frac{3}{4}$. is this the same as the slope of line p?
remember, the slope of line p is $\frac{3}{4}$.
slope = $\frac{vertical distance}{horizontal distance}$
= $\frac{5 - 2}{3 - 7}$
= $\frac{3}{-4}$
= $-\frac{3}{4}$

Explanation:

Step1: Recall slope definition

The standard slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $\frac{y_2 - y_1}{x_2 - x_1}$ (or $\frac{y_1 - y_2}{x_1 - x_2}$, as reversing both numerator and denominator preserves the sign/value).

Step2: Compare calculated value to given slope

The given slope of line $p$ is $\frac{3}{4}$. The calculated value is $-\frac{3}{4}$. These two values are not equal, because the order of subtraction for the x-values was reversed without reversing the y-values consistently in the standard slope calculation.

Answer:

No, $-\frac{3}{4}$ is not the same as the slope of line $p$. The correct slope is $\frac{3}{4}$, and the error came from inconsistent subtraction order of x and y coordinates.