Answered

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A line perpendicular to f(x) = 3x + 4 and passing through the
point (3,1)

What’s the slope and the equation of the?

Sagot :

rspill6

Answer:

y = -(1/3)x + 2

Step-by-step explanation:

A perpendicular line has a slope that is the negative inverse of the reference line.  For a line with slope of 3, the perpendicular line would have a slope of -(1/3).  That brings us to an equation of the slope-intercept form of:

y = -(1/3)x + b

Any equation having this form will be perpendicular to y = 3x + 4.

We could pick any value for b and the line will be perpendicular.  The b value will only shift the graph up or down, not change the slope.  But we are told that this line must go through point (3,1), so we need to pick a value of b that will make this happen.

To do this, enter the point (3,1) into the equation and solve for b:

y = -(1/3)x + b

1 = -(1/3)*3 + b    

1 = -1 + b

b = 2

The equation of a line perpendicular to y = 3x + 4 that goes through point (3,1) is:

y = -(1/3)x + 2

See attached image.

View image rspill6
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