How do you find a standard form equation for the line with A(5, 6) and is perpendicular to the line 4x+3y=8?

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Answer 1 · 2018-05-18T11:03:19

Therefore standard form of the perpendicular line thru A (5,6) is

#color(green)(3x - 4y = -9#

#4x + 3y = 8#

#3y = -4x + 8#

#y = (-4/3)x + 8#, in slope - intercept form.

Slope #m_1 = -4/3#

Slope of perpendicular line #m_2 = -1/m_1 = 3/4#

Equation of perpendicular line passing thru A(5,6) is given by

#(y - y_A) = m_2 * (x - x_A)#

#(y - 6) = (3/4)* (x - 5)#

#(4y - 24) = (3x - 15)#

Standard form of a linear equation is given by

#ax + by = c#

Therefore standard form of the perpendicular line thru A (5,6) is

#color(green)(3x - 4y = -9#