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

A. [tex]-\frac{4}{3}[/tex]
B. [tex]-\frac{3}{4}[/tex]
C. [tex]\frac{1}{2}[/tex]
D. 2


Sagot :

To find the slope of the line that goes through the points [tex]$(1, -5)$[/tex] and [tex]$(4, 1)$[/tex], we can use the formula for the slope of a line given two points \((x_1, y_1)\) and \((x_2, y_2)\). The formula for the slope \(m\) is:

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

Here, our points are \((1, -5)\) and \((4, 1)\). Let's substitute these points into the formula:

1. Identify the coordinates:
[tex]\[ x_1 = 1, \quad y_1 = -5, \quad x_2 = 4, \quad y_2 = 1 \][/tex]

2. Substitute the coordinates into the slope formula:
[tex]\[ m = \frac{1 - (-5)}{4 - 1} \][/tex]

3. Simplify the numerator and the denominator:
[tex]\[ m = \frac{1 + 5}{4 - 1} = \frac{6}{3} \][/tex]

4. Divide the numerator by the denominator:
[tex]\[ m = \frac{6}{3} = 2 \][/tex]

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

The correct answer is:
D. 2
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