Verified answer

First, its slope is –1/3 because it is perpendicular.

Its equation is y = –1/3(x – 2) + 7 Point-slope form thru (2,7)

Just multiply it out to get slope-intercept form:

y = –1/3x + 2/3 + 7

y = –1/3x + 23/3 (since 7 = 21/3)

Comment: Most people start with the slope-intercept form. Plug in m, (x,y), then solve for b and then reform. The way I showed you is faster. If a line have slope m and passes through (a.c) its equation is automatically y = m(x – a) + c. It is worth memorizing. You get an equation instantly with no work. Then you merely have to change the form, if you need to. It looks similar to y = mx+ b, except for subtracting the a inside the parentheses.

The slope-intercept form of an equation of a straight line is y = mx + b, where m = slope and b = y-intercept.

For the equation y = 3x - 4, slope m = 3.

A perpendicular line will have slope equal to the negative inverse of the slope of the original line:

m1 = 3

m2 = -1/3

Basic equation for perpendicular line:

y = - 1/3 + b

Calculate b using the point (2, 7)

b = y - mx

b = 7 - [- 1/3(2)]

b = 7 + 2/3

b = 23/3

Equation of perpendicular line through (2, 7):

y = - 1/3 x + 23/3

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Perpendicular slopes are opposite reciprocal, so your new slope would be -1/3. Now plug in the slope and the given point into y=mx+b.

7=-1/3(2)+b

7=-2/3+b

b=7 2/3

Plug back into y=mx+b.

y=-1/3x+7 2/3

the slope would be -1/3 since it's perpendicular.

then you would do:

(y-7)= -1/3 (x-2) using the coordinate point that was given

and solve algebraically,

y = -1/3x + 2/3 +7

and it equals

y = -1/3 + 23/7

:)