The equation of the parallel line is y = –2x – 11.
Solution:
Given equation of the line is y = –2x – 5.
Slope of this line is [tex](m_1)[/tex] = –2
To write the equation parallel to this line and passes through (–4, –3).
If two lines are parallel, then they have the same slope.
[tex]\Rightarrow m_1=m_2[/tex]
[tex]\Rightarrow m_2 =-2[/tex]
Point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute the given values in the formula, we get
[tex]y-(-3)=-2(x-(-4))[/tex]
[tex]y+3=-2(x+4)[/tex]
[tex]y+3=-2x-8[/tex]
Subtract 3 from both sides of the equation.
[tex]y+3-3=-2x-8-3[/tex]
[tex]y=-2x-11[/tex]
Hence the equation of the parallel line is y = –2x – 11.
