Respuesta :
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]