Answered

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Multiple Choice

What is the slope of the line that passes through the points [tex][tex]$(-2,5)$[/tex][/tex] and [tex][tex]$(1,4)$[/tex][/tex]?

A. [tex][tex]$-3$[/tex][/tex]
B. [tex][tex]$-2$[/tex][/tex]
C. [tex][tex]$-\frac{1}{3}$[/tex][/tex]
D. [tex][tex]$\frac{1}{3}$[/tex][/tex]

Sagot :

GinnyAnswer
To find the slope of the line that passes through the points [tex]\((-2, 5)\)[/tex] and [tex]\((1, 4)\)[/tex], we use the slope formula:

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

where [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are coordinates of the two points.

Here, [tex]\((x_1, y_1) = (-2, 5)\)[/tex] and [tex]\((x_2, y_2) = (1, 4)\)[/tex].

Substituting these values into the formula, we get:

[tex]\[ m = \frac{4 - 5}{1 - (-2)} \][/tex]

Simplifying the numerator (4 - 5) and the denominator (1 - (-2)), we get:

[tex]\[ m = \frac{-1}{1 + 2} \][/tex]

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

Thus, the slope of the line that passes through the points [tex]\((-2, 5)\)[/tex] and [tex]\((1, 4)\)[/tex] is:

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

So the correct answer is:

[tex]\[ -\frac{1}{3} \][/tex]
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