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

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

Sagot :

GinnyAnsweridn
To find the equation of a line in point-slope form, you will need two things: the slope of the line and a point that the line passes through. The point-slope form of a line is given by the formula:

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

where:
- [tex]\( m \)[/tex] is the slope of the line,
- [tex]\((x_1, y_1) \)[/tex] is a point that the line passes through.

We are given:
- The slope [tex]\(m = 3\)[/tex],
- The point [tex]\((x_1, y_1) = (2, 1)\)[/tex].

Plug these values into the point-slope form equation:

[tex]\[ y - 1 = 3(x - 2) \][/tex]

So, the point-slope form of the line with slope 3 that passes through the point [tex]\((2, 1)\)[/tex] is:

[tex]\[ y - 1 = 3(x - 2) \][/tex]

Comparing this with the provided options:

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

The correct answer is option A:

[tex]\[ y-1=3(x-2) \][/tex]

Thus, the correct answer is A.
Wegnerkolmp2741oidn

Answer:

A. y - 1 = 3(x - 2)

Step-by-step explanation:

The point slope form of a line is given by

y-y1 = m(x-x1) where m is the slope of a line and (x1,y1) is a point on the line.

We know that the slope is 3 and a point on the line is (2,1)

y - 1 = 3(x - 2)

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