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write the equation of a line that is perpendicular to the line y=-3/4x+3 and passes through the point (3,7). Write your answer in BOTH point-slope form and slope-intercept form

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Answer:

see explanation

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - [tex]\frac{3}{4}[/tex] x + 3 ← is in slope- intercept form

with slope m = - [tex]\frac{3}{4}[/tex]

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-\frac{3}{4} }[/tex] = [tex]\frac{4}{3}[/tex] , then

y = [tex]\frac{4}{3}[/tex] x + c ← is the partial equation

To find c substitute (3, 7 ) into the partial equation

7 = 4 + c ⇒ c = 7 - 4 = 3

y = [tex]\frac{4}{3}[/tex] x + 3 ← in slope- intercept form

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b ) a point on the line

Here m = [tex]\frac{4}{3}[/tex] and (a, b ) = (3, 7 ) , then

y - 7 = [tex]\frac{4}{3}[/tex] (x - 3) ← in point- slope form

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