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On a coordinate plane, a line goes through (negative 5, negative 4) and (0, negative 3). A point is at (negative 2, 2). What is the equation of the line that is parallel to the given line and passes through the point (–2, 2)? y = One-fifthx + 4 y = One-fifthx + Twelve-fifths y = –5x + 4 y = –5x + Twelve-fifths

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Answer:

Second option: [tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

We know that a line goes through the points [tex](-5,-4)[/tex] and [tex](0,-3)[/tex]

Since the line intersects the y-axis when [tex]x=0[/tex], then the y-intercept of this line is:

[tex]b=-3[/tex]

Substitute the y-intercept and coordinates of the point  [tex](-5,-4)[/tex] into the equation [tex]y=mx+b[/tex] and solve for "m":

[tex]-4=m(-5)-3\\\\-4+3=-5m\\\\m=\frac{-1}{-5}\\\\m=\frac{1}{5}[/tex]

By definition, the slopes of parallel lines are equal, then the slope of the other line is:

[tex]m=\frac{1}{5}[/tex]

Knowing that it passes through the point [tex](-2, 2)[/tex], we can substitute values into the equation  [tex]y=mx+b[/tex] and solve for "b":

 [tex]2=\frac{1}{5}(-2)+b\\\\2+\frac{2}{5}=b\\\\b=\frac{12}{5}[/tex]

Therefoe, the equation of this line is:

 [tex]y=\frac{1}{5}x+\frac{12}{5}[/tex]

Answer:

(B) y=1/5x +12/5

Step-by-step explanation:

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