# y=1/2x-9 Find the line that's perpendicular to it and passes through

$$\displaystyle{y}=\frac{{1}}{{2}}{x}-{9}$$
Find the line that's perpendicular to it and passes through (7,10)

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pivonie8
First, find the slope using the formula:
y=mx+b
Substitute
$$\displaystyle{y}=\frac{{1}}{{2}}{x}-{9}$$
$$\displaystyle{m}=\frac{{1}}{{2}}$$
Perpendicular lines have negative reciprocal slopes, therefore the needed line will have a slope of -2.
Point slope form:
$$\displaystyle{y}-{\underset{{{1}}}{{{y}}}}={m}{\left({x}-{\underset{{{1}}}{{{x}}}}\right)}$$
Substitute given coordinates:
y-10=-2(x-7)
y-10=-2x+14
y=-2x+24