Question

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

Answer 1

Answer:

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

Step-by-step explanation:

Answer 2

Answer:

$y=-\frac{1}{2}x+2$

Step-by-step 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:

$m_2=-\frac{1}{2}$

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:

$y-5=-\frac{1}{2}(x-(-6))$

Simplify:

$y-5=-\frac{1}{2}(x+6)$

Distribute:

$y-5=-\frac{1}{2}x-3$

Add 5 to both sides:

$y=-\frac{1}{2}x+2$

So, our equation is:

$y=-\frac{1}{2}x+2$