Respuesta :
Answer:
y=-0.6x+3.4
Explanation:
First, by definition, two lines are parallel if they have the same slope.
Given the equation of the line:
[tex]-3x-5y=-6[/tex]We find the slope by rewriting the line in the slope-intercept form:
[tex]y=mx+b\text{ where }\begin{cases}m={Slope} \\ b={y-intercept}\end{cases}[/tex]This gives:
[tex]\begin{gathered} -3x+6=5y \\ y=-\frac{3x}{5}+\frac{6}{5} \\ \implies\text{ The slope}=-\frac{3}{5} \end{gathered}[/tex]Since the two lines are to be parallel, the new line will have a slope of -3/5 and pass through the point (-4,1).
Substitute x=-4, y=1 and m=-3/5 into the slope-intercept form:
[tex]\begin{gathered} y=mx+b \\ 1=-4(\frac{3}{5})+b \\ b=1+\frac{12}{5} \\ b=3.4 \end{gathered}[/tex]The equation of the line is:
[tex]\begin{gathered} y=-\frac{3}{5}x+\frac{17}{5} \\ y=-0.6x+3.4 \end{gathered}[/tex]