What is the slope of the line passing through the points [tex]$(7,6)$[/tex] and [tex]$(-2,-9)$[/tex]?

A. [tex]\frac{5}{3}[/tex]
B. [tex]\frac{3}{5}[/tex]
C. [tex]-\frac{5}{3}[/tex]
D. [tex]-3[/tex]



Answer :

To find the slope of the line passing through the points [tex]\((7,6)\)[/tex] and [tex]\((-2, -9)\)[/tex], we use the formula for the slope between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:

[tex]\[ \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

Given the points [tex]\((x_1, y_1) = (7, 6)\)[/tex] and [tex]\((x_2, y_2) = (-2, -9)\)[/tex], we can substitute these values into the slope formula:

[tex]\[ \text{slope} = \frac{-9 - 6}{-2 - 7} \][/tex]

First, simplify the numerator and the denominator:

[tex]\[ -9 - 6 = -15 \][/tex]

[tex]\[ -2 - 7 = -9 \][/tex]

Now, we have:

[tex]\[ \text{slope} = \frac{-15}{-9} \][/tex]

Simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 3:

[tex]\[ \text{slope} = \frac{-15 \div 3}{-9 \div 3} = \frac{-5}{-3} = \frac{5}{3} \][/tex]

So, the slope of the line passing through the points [tex]\((7, 6)\)[/tex] and [tex]\((-2, -9)\)[/tex] is:

[tex]\[ \boxed{\frac{5}{3}} \][/tex]