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If a line has a slope of 4 and contains the point [tex]\((-2, 5)\)[/tex], what is its equation in point-slope form?

A. [tex]\(y + 2 = 4(x - 5)\)[/tex]
B. [tex]\(y - 5 = 4(x + 2)\)[/tex]
C. [tex]\(y + 5 = 4(x - 2)\)[/tex]
D. [tex]\(y - 5 = 4(x - 2)\)[/tex]

Sagot :

GinnyAnsweridn
To find the equation of a line in point-slope form given the slope and a point on the line, you can use the point-slope 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 the given point on the line.

In this case, the slope ([tex]\( m \)[/tex]) is 4 and the point ([tex]\( x_1, y_1 \)[/tex]) is [tex]\((-2, 5)\)[/tex].

Let's substitute the values into the point-slope formula:

[tex]\[ y - 5 = 4(x - (-2)) \][/tex]

Simplify the equation:

[tex]\[ y - 5 = 4(x + 2) \][/tex]

Thus, the equation of the line in point-slope form is:

[tex]\[ y - 5 = 4(x + 2) \][/tex]

By comparing this with the given options:
- A. [tex]\( y + 2 = 4(x - 5) \)[/tex]
- B. [tex]\( y - 5 = 4(x + 2) \)[/tex]
- C. [tex]\( y + 5 = 4(x - 2) \)[/tex]
- D. [tex]\( y - 5 = 4(x - 2) \)[/tex]

We see that the correct answer is:
B. [tex]\( y - 5 = 4(x + 2) \)[/tex]

Therefore, the correct option is B.
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