What is an equation of the line that passes through the point (8,-7)(8,−7) and is parallel to the line x+2y=18x+2y=18?

Linear equations are typically organized in slope-intercept form: [tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
Parallel lines always have the same slope (m) and different y-intercepts (b)

1) Determine the slope (m)

[tex]x+2y=18[/tex]

Rearrange this equation into slope-intercept form (this will make it easier for us to identify the slope)

Subtract x from both sides to isolate 2y

[tex]x+2y-x=-x+18\\2y=-x+18[/tex]

Divide both sides by 2 to isolate y

[tex]y=-\frac{1}{2} x+9[/tex]

Now, we can see clearly that [tex]-\frac{1}{2}[/tex] is in the place of m. Because parallel lines have the same slope, [tex]-\frac{1}{2}[/tex] is therefore the slope of the line we're currently solving for. Plug [tex]-\frac{1}{2}[/tex] into [tex]y=mx+b[/tex]:

[tex]y=-\frac{1}{2} x+b[/tex]

2) Determine the y-intercept

[tex]y=-\frac{1}{2} x+b[/tex]

Plug in the point (8,-7)

[tex]-7=-\frac{1}{2} (8)+b\\-7=-4+b[/tex]

Add 4 to both sides

[tex]-7+4=-4+b+4\\-3=b[/tex]

Therefore, the y-intercept is -3. Plug this back into [tex]y=-\frac{1}{2} x+b[/tex]:

[tex]y=-\frac{1}{2} x-3[/tex]

I hope this helps!