Question

7. Determine whether y varies directly with x. If so, find the constant of variation and write the equation.42-41-24X-2

Answer 1

We have to find two points from the graph to find the slope of the line equation:

`m=(y_2-y_1)/(x_2-x_1)=(0-2)/(0-(-4))=-(2)/(4)=-(1)/(2)`

We took the points (-4, 2) and (0, 0)

x1 = -4

y1 = 2

x2 = 0

y2 = 0

Then, using the point-slope form of the line equation, we have, for point (0, 0):

`y-0=-(1)/(2)(x-0)\Rightarrow y=-(1)/(2)x`

Then, the constant of variation is k = -1/2 and y = (-1/2)x.