What is the slope of the line that is perpendicular to the line whose equation is 2x + y = 4?
The slope of a curve is defined as the change in the vertical direction divided by the change in the horizontal direction. Slopes can also be found by using the first derivative of the given function.
Answer: The slope of the line that is perpendicular to the line 2x + y = 4 is 1/2.
Let's understand the solution in detail.
The equation of the given line ⇒ 2x + y = 4
We know that for a line to be perpendicular to another line, the product of its slopes must be equal to -1, i.e, m1m2 = -1
Hence, after we rearrange the given equation in the form of y = m1x + c, we get y = -2x + 4.
Hence, m1 = -2.
Therefore, we have a slope of the given line = -2
Now, we use the above property of perpendicular lines mentioned.
⇒ m1m2 = -1
⇒ m2 = -1/m1 = -1/2