Question

1. the slope of the line determined by a (2, -3) and b (-1, 3) is

a) -2
b) $-\frac{1}{2}$
c) $\frac{1}{2}$
d) 2

Explanation:

Step1: Recall slope formula

The slope $m$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2-y_1}{x_2-x_1}$

Step2: Assign values to variables

Let $(x_1,y_1)=(2,-3)$ and $(x_2,y_2)=(-1,3)$. Substitute into formula:
$m=\frac{3-(-3)}{-1-2}$

Step3: Simplify numerator and denominator

$m=\frac{3+3}{-3}=\frac{6}{-3}$

Step4: Calculate final slope

$m=-2$

Answer:

a) -2