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What is the slope of the line represented by the equation [tex][tex]$y - 6 = 5(x - 2)$[/tex][/tex]?

A. 2
B. -5
C. 6
D. 5

Sagot :

GinnyAnswer
To determine the slope of the line represented by the equation [tex]\( y - 6 = 5(x - 2) \)[/tex], let's start by examining the equation in more detail.

The given equation is in the point-slope form of a line, which is expressed as:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]

In the point-slope form:
- [tex]\((x_1, y_1)\)[/tex] is a point on the line.
- [tex]\(m\)[/tex] is the slope of the line.

Let's compare the given equation [tex]\( y - 6 = 5(x - 2) \)[/tex] with the standard form [tex]\( y - y_1 = m(x - x_1) \)[/tex].

From this comparison, we can identify:
- [tex]\( y_1 = 6 \)[/tex]
- [tex]\( x_1 = 2 \)[/tex]
- [tex]\( m = 5 \)[/tex] (the coefficient of [tex]\((x - 2)\)[/tex])

Therefore, the slope of the line is:
[tex]\[ m = 5 \][/tex]

The correct answer is:
D. 5
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