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What is the point-slope form of a line with slope 3 that contains the point [tex][tex]$(2,1)$[/tex][/tex]?

A. [tex]y-2=3(x-1)[/tex]
B. [tex]y+1=3(x+2)[/tex]
C. [tex]y-2=3(x+1)[/tex]
D. [tex]y-1=3(x-2)[/tex]

Sagot :

GinnyAnswer
Sure, let's find the point-slope form of a line given a slope and a specific point.

First, recall the point-slope form of a line, which is:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
Here, [tex]\( m \)[/tex] is the slope and [tex]\( (x_1, y_1) \)[/tex] is the given point on the line.

In this problem, we have:
- Slope ([tex]\( m \)[/tex]) = 3
- Point ([tex]\( x_1, y_1 \)[/tex]) = (2, 1)

Substitute these values into the point-slope form equation:
[tex]\[ y - 1 = 3(x - 2) \][/tex]

So, the correct point-slope form of the line is:
[tex]\[ y - 1 = 3(x - 2) \][/tex]

Looking at the answer choices, the correct option is:
D. [tex]\( y - 1 = 3(x - 2) \)[/tex]
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