Name the constant of variation for each question. Then determine the slope of the line that passes through each pair of point.
y=2x
The formula for direct variation is y = kx, where k is the constant of variation.
For slope, use y - y1 = m(x-x1)
m=1/2
m= 1/4
The constant of variation in the equation y=2x is 2.
To determine the slope of the line that passes through a pair of points, you can use the formula:
slope = (y₂ - y₁) / (x₂ - x₁)
Let's take two arbitrary points and calculate the slope:
Point 1: (x₁, y₁)
Point 2: (x₂, y₂)
For example, let's consider the points (1, 2) and (3, 6):
x₁ = 1, y₁ = 2
x₂ = 3, y₂ = 6
slope = (6 - 2) / (3 - 1)
= 4 / 2
= 2
So, the slope of the line that passes through the points (1, 2) and (3, 6) is 2.