write an equation

Question

Write an equation for a linear function whose graph has the given characteristics.
Passes through (42, 0), perpendicular to the graph of
g(x) = 7x + 3

Answer 1

This problem is going to utilize the point-slope formula:

 

y - y₁ = m ( x - x₁ )

 

We need to plug our values into this formula. Since it passes through ( 42 , 0 ), we can plug these values in.

 

y - 0 = m ( x - 42 )

 

To find the slope, you need to use the slope of g(x) = 7x + 3. The slope of this line is 7. The products of the slopes of two perpendicular lines is -1. That means the slope of the perpendicular line we're looking for is -1/7. Plug this in.

 

y - 0 = ( -1 / 7 )( x - 42 )

 

Solve for y. Distribute. That leaves you with your answer: 

 

y = ( -1 / 7 )x + 6

 

 

Answer 2

First thing, you get the slope which is -1/7. Then you write it in y=mx+b form.

y=-1/7x+b then solve for b by substituting 42 and 0 for x and y respectively

0 = -1/7(42) + b

b=42/7=6

 

Therefore y=-1/7x + 6 is your equation