The equation of the line parallel to 8x – 16y = –14 and passes through (3, 0) is [tex]y=\frac{1}{2}x-\frac{3}{2}[/tex].
Solution:
Parallel line:
8x – 16y = –14
Subtract 8x on both sides,
–16y = –8x – 14
Divide by –16 on both sides, we get
[tex]$y=\frac{8}{16}x+\frac{14}{16}[/tex]
[tex]$m_1=\frac{8}{16}[/tex]
Slope of this line is [tex]\frac{8}{16}[/tex].
Slopes of the parallel lines are equal.
[tex]m_1=m_2[/tex]
[tex]$m_2=\frac{8}{16}[/tex]
The line passes through the point (3, 0).
[tex]x_1=3, y_1=0[/tex]
Point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]$y-0=\frac{8}{16} (x-3)[/tex]
[tex]$y=\frac{8}{16}x-\frac{24}{16}[/tex]
[tex]$y=\frac{1}{2}x-\frac{3}{2}[/tex]
The equation of the line parallel to 8x – 16y = –14 and passes through (3, 0) is [tex]y=\frac{1}{2}x-\frac{3}{2}[/tex].
