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

Sagot :

GinnyAnsweridn
To determine the point-slope form of a line with a given slope and point, we use the point-slope formula:

[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.

Given:
- Slope ([tex]\( m \)[/tex]) = -3
- Point ([tex]\( x_1, y_1 \)[/tex]) = (10, -1)

Plug these values into the point-slope formula:

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

Simplify the equation:

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

Hence, the point-slope form of the line is:

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

So, the correct answer is:

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