Question

Write an equation for a line perpendicular to y=2x+5 and passing through the point (-6,5)

Answer 1

5 would be on your Y axis (go up two numbers from 5, go to the right 1 and draw a dot then connect your lines

Explanation:

Answer 2

`y=-(1)/(2)x+2`

Explanation:

So we want to find the equation of a line perpendicular to y=2x+5 and passes through the point (-6,5).

First, let's determine the slope of our equation. Remember that the slopes of perpendicular lines are negative reciprocals. In other words:

`m_1\cdot m_2=-1`

To find our slope, let's substitute 2 (the slope of y=2x+5) for m₁ and solve for m₂. So:

`2\cdot m_2=-1`

Divide both sides by 2:

`m_2=-(1)/(2)`

Therefore, the slope of our new line is -1/2.

Now, we can use the point-slope form to find the equation of our line. The point-slope form is:

`y-y_1=m(x-x_1)`

Where m is the slope and (x₁, y₂) is a point.

So, let's substitute -1/2 for m and (-6,5) for (x₁, y₂), respectively. So:

`y-5=-(1)/(2)(x-(-6))`

Simplify:

`y-5=-(1)/(2)(x+6)`

Distribute:

`y-5=-(1)/(2)x-3`

Add 5 to both sides:

`y=-(1)/(2)x+2`

So, our equation is:

`y=-(1)/(2)x+2`