Respuesta :
To write the equation of the given line:
1. Find the slope (m), use the parallel line as parallel lines have the same slope.
Write the equation of the parallel line in slope intercept form (y=mx+b) to identify the slope:
[tex]\begin{gathered} -x+8y=16 \\ 8y=x+16 \\ y=\frac{1}{8}x+\frac{16}{8} \\ \\ y=\frac{1}{8}x+2 \end{gathered}[/tex]Slope: 1/8
2. Use the given point and the slope to find the y-intercept (b):
[tex]\begin{gathered} (-8,-8);x=-y,y=-8 \\ m=\frac{1}{8} \\ \\ y=mx+b \\ -8=\frac{1}{8}(-8)+b \\ \\ -8=-1+b \\ -8+1=b \\ \\ b=-7 \end{gathered}[/tex]3. Write the equation in slope-intercept form:
[tex]y=\frac{1}{8}x-7[/tex]2. Leave the terms with variable in left side of the equal to write the equation in standard form:
[tex]y-\frac{1}{8}x=-7[/tex]_________
Answer: