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Question 10 of 40

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

Sagot :

GinnyAnsweridn
Absolutely! Let's work through the question step-by-step.

We know that the line has a slope ([tex]\( m \)[/tex]) of 4 and it passes through the point [tex]\((-2, 5)\)[/tex].

The point-slope form of the equation of a line is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]

Here:
- [tex]\( m = 4 \)[/tex]
- [tex]\( (x_1, y_1) = (-2, 5) \)[/tex]

We substitute these values into the point-slope form equation:

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

Simplify the expression inside the parentheses:
[tex]\[ y - 5 = 4(x + 2) \][/tex]

Therefore, the equation of the line in point-slope form is:
[tex]\[ \boxed{y - 5 = 4(x + 2)} \][/tex]

The correct option is:
A. [tex]\( y - 5 = 4(x + 2) \)[/tex]
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