Find an equation of the line perpendicular to the graph of 14x-7y=4 that passes through the point at (2,-9)

If it is perpendicular to the line 14x-7y=4, then we know our line has the opposite and inverse slope of that line. Solving for y of the first line, we get y=2x-(4/7). All we care about is the coefficient of the x term, because that will give us our slope. The slope of the first line is 2, so the slope of out line is the opposite and inverse of that slope, which -(1/2).

Plugging into our slope- point formula, where y1=(-9), x1=2, and m=(-1/2), then:

y-(-9)=(-1/2)(x-2)
y+9=(-1/2)x+1
y=(-1/2)x-8

Hope this helps!