Indicate the equation of the given line in standard form.

The line through point (-3, 4) and perpendicular to a line that has slope 2/5

Question

Indicate the equation of the given line in standard form.

The line through point (-3, 4) and perpendicular to a line that has slope 2/5

anonymous · Answer

Right, you have a point, and you need a gradient so you may then use the point-gradient formula for a straight line.

You're told that the line perpendicular to yours has slope $$m_1=\frac{2}{5}$$Two lines are perpendicular if their gradients satisfy the following condition,$$m_1m_2=-1$$This means your gradient must be$$m_2=\frac{-1}{m_1}=-\frac{1}{\frac{2}{5}}=-\frac{5}{2}$$

anonymous · Answer

The point-gradient formula then gives,$$y-y_1=m(x-x_1)$$which here becomes,$$y-4=-\frac{5}{2}(x-(-3)) \rightarrow 2(y-4)=-5(x+3)$$after multiplying both sides by 2.  Expanding and collecting terms, you have$$2y-8=-5x-15 \rightarrow 5x+2y=-7$$

anonymous · Answer

The last equation is your equation in standard form:$$Ax+By=C$$

anonymous · Answer

Thank you so much!

anonymous · Answer

np.  Just hope it's clear enough for you to do it for yourself next time :)