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What is the point-slope form of a line with slope [tex]\(-3\)[/tex] that contains the point [tex]\((10, -1)\)[/tex]?

A. [tex]\(y + 1 = 3(x - 10)\)[/tex]
B. [tex]\(y + 1 = -3(x - 10)\)[/tex]
C. [tex]\(y + 1 = 3(x + 10)\)[/tex]
D. [tex]\(x + 1 = -3(y - 10)\)[/tex]

Sagot :

GinnyAnswer
To determine the point-slope form of the line with a given slope and passing through a given point, we use the point-slope form equation of a line:

[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 on the line

Given:
- The slope [tex]\( m = -3 \)[/tex]
- The point [tex]\((x_1, y_1) = (10, -1)\)[/tex]

Substituting these values into the point-slope form equation:

[tex]\[ y - (-1) = -3(x - 10) \][/tex]

This simplifies to:

[tex]\[ y + 1 = -3(x - 10) \][/tex]

Thus, the point-slope form of the line with a slope of -3 passing through the point (10, -1) is:

[tex]\[ y + 1 = -3(x - 10) \][/tex]

Comparing this with the given options:
- A. [tex]\( y+1=3(x-10) \)[/tex]
- B. [tex]\( y+1=-3(x-10) \)[/tex]
- C. [tex]\( y+1=3(x+10) \)[/tex]
- D. [tex]\( x+1=-3(y-10) \)[/tex]

The correct answer is:

[tex]\[ \boxed{B} \][/tex]
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