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The equation of a line in point-slope form is shown below:

[tex]\[ y - 9 = \frac{1}{5}(x - 2) \][/tex]

What is the slope of this line?

A. 2
B. [tex]\(\frac{1}{9}\)[/tex]
C. 5
D. [tex]\(\frac{1}{5}\)[/tex]

Sagot :

GinnyAnswer
To find the slope of the line given in point-slope form, let's examine the equation:

[tex]\[ y - 9 = \frac{1}{5}(x - 2) \][/tex]

The point-slope form of a line is given by:

[tex]\[ y - y_1 = m(x - x_1) \][/tex]

where [tex]\((x_1, y_1)\)[/tex] is a point on the line and [tex]\(m\)[/tex] is the slope.

From the given equation:

[tex]\[ y - 9 = \frac{1}{5}(x - 2) \][/tex]

we can see that [tex]\((x_1, y_1)\)[/tex] is [tex]\((2, 9)\)[/tex] and the slope [tex]\(m\)[/tex] is [tex]\(\frac{1}{5}\)[/tex].

Therefore, the slope of the line is:

[tex]\[ m = \frac{1}{5} \][/tex]

The correct answer is:
D. [tex]\(\frac{1}{5}\)[/tex]
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