Find the slope of the line passing through the points [tex][tex]$(-6, 6)$[/tex][/tex] and [tex][tex]$(4, -7)$[/tex][/tex].



Answer :

To find the slope of the line passing through the points [tex]\((-6, 6)\)[/tex] and [tex]\((4, -7)\)[/tex], you can use the slope formula. The slope [tex]\( m \)[/tex] of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:

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

Here, the coordinates of the two points are:
[tex]\[ (x_1, y_1) = (-6, 6) \][/tex]
[tex]\[ (x_2, y_2) = (4, -7) \][/tex]

Substituting these values into the slope formula, we get:

[tex]\[ m = \frac{-7 - 6}{4 - (-6)} \][/tex]

First, calculate the numerator [tex]\((y_2 - y_1)\)[/tex]:
[tex]\[ y_2 - y_1 = -7 - 6 = -13 \][/tex]

Next, calculate the denominator [tex]\((x_2 - x_1)\)[/tex]:
[tex]\[ x_2 - x_1 = 4 - (-6) = 4 + 6 = 10 \][/tex]

So, the slope [tex]\( m \)[/tex] is:
[tex]\[ m = \frac{-13}{10} = -1.3 \][/tex]

Therefore, the slope of the line passing through the points [tex]\((-6, 6)\)[/tex] and [tex]\((4, -7)\)[/tex] is [tex]\(\boxed{-1.3}\)[/tex].