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What is the slope of the line that contains the points [tex]$(-3, -1)$[/tex] and [tex]$(3, -10)$[/tex]?

A. Undefined
B. 0
C. [tex]$-\frac{2}{3}$[/tex]
D. [tex]$-\frac{3}{2}$[/tex]


Sagot :

To determine the slope of the line that passes through the points [tex]\((-3, -1)\)[/tex] and [tex]\( (3, -10) \)[/tex], we 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, our points are [tex]\((x_1, y_1) = (-3, -1)\)[/tex] and [tex]\((x_2, y_2) = (3, -10)\)[/tex].

Substitute the coordinates into the slope formula:

[tex]\[ m = \frac{-10 - (-1)}{3 - (-3)} \][/tex]

Simplify the numerator and the denominator:

[tex]\[ m = \frac{-10 + 1}{3 + 3} \][/tex]
[tex]\[ m = \frac{-9}{6} \][/tex]

Simplify the fraction:

[tex]\[ m = \frac{-9}{6} = -\frac{3}{2} \][/tex]

Hence, the slope of the line that contains the points [tex]\((-3, -1)\)[/tex] and [tex]\((3, -10)\)[/tex] is [tex]\( -\frac{3}{2} \)[/tex].

Correct answer: [tex]\( -\frac{3}{2} \)[/tex]