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Which equation represents a line that passes through [tex]\((-2, 4)\)[/tex] and has a slope of [tex]\(\frac{2}{5}\)[/tex]?

A. [tex]\(y - 4 = \frac{2}{5}(x + 2)\)[/tex]

B. [tex]\(y + 4 = \frac{2}{5}(x - 2)\)[/tex]

C. [tex]\(y + 2 = \frac{2}{5}(x - 4)\)[/tex]

D. [tex]\(y - 2 = \frac{2}{5}(x + 4)\)[/tex]

Sagot :

GinnyAnsweridn
To determine the equation of a line that passes through the point [tex]\((-2, 4)\)[/tex] and has a slope of [tex]\(\frac{2}{5}\)[/tex], we can use the point-slope form of the equation of a line, which is given by:

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

Here,
[tex]\( (x_1, y_1) = (-2, 4) \)[/tex] is the given point, and
[tex]\( m = \frac{2}{5} \)[/tex] is the given slope.

Plugging these values into the point-slope form gives:

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

Since [tex]\( x - (-2) = x + 2 \)[/tex], the equation simplifies to:

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

Therefore, the equation that represents the line passing through [tex]\((-2, 4)\)[/tex] with a slope of [tex]\(\frac{2}{5}\)[/tex] is:

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

So, the correct answer is:

[tex]\[ \boxed{y - 4=\frac{2}{5}(x+2)} \][/tex]
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