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Answer 1

In Coordinate Geometry, slope, or also known as the gradient, can be found using this formula:

$\text{Slope =} \dfrac{Y_{2} - Y_{2} }{X_{2} - X_{1}}$

Find the slope of A(4, -6), B(7, 2):

$\text{Slope =} \dfrac{Y_{2} - Y_{2} }{X_{2} - X_{1}}$

$\text{Slope =} \dfrac{2-(-6)}{7-4}$

$\text{Slope =} \dfrac{8}{3}$

Find the slope of A(-2, -5), B(1, -7):

$\text{Slope =} \dfrac{Y_{2} - Y_{2} }{X_{2} - X_{1}}$

$\text{Slope =} \dfrac{-7-(-5)}{1-(-2)}$

$\text{Slope =} -\dfrac{2}{3}$

Answer 2

Solution

The above questions can be solved by using two point formula

$\sf M = \dfrac{Y_2 - Y_1}{X_2 - X_1}$

1. Given Points are A(4,-6) and B(7,2)

Substituting the values,

$\implies \: \sf \: m = \dfrac{2 - ( - 6)}{7 - 4} \\ \\ \implies \: \sf \: m = \dfrac{2 + 6}{3} \\ \\ \implies \: \underline{ \boxed{\sf \: m = \dfrac{8}{3} }}$

• Slope of AB is 8/3

2. Given Points are A(-2,-5) and B(1,-7)

Substituting the values,

$\implies \: \sf \: m = \dfrac{ - 7 - (5)}{1 - ( - 2)} \\ \\ \implies \: \underline{ \boxed{\sf \: m = - \dfrac{2}{3} }}$

• Slope of AB is -2/3