Answer :
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]
[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]
