Answer:
"The relationship is proportional."
"The relationship is proportional."
"The equation of the line is y = -3x"
Step-by-step explanation:
First, a proportional relationship can be written as:
y = k*x
where k is called the constant of proportionality. (or the slope)
You can see that if we take x = 0, we have
y = k*0 = 0
Then this type of line always passes through the point (0, 0).
And in the graph you can see that this line does that, then:
"The relationship is proportional." is true.
We also can see that as x increases, the value of y decreases, this must imply that k is a negative number, then:
"The slope is negative." is true.
To find the value of the slope, we can take two points that belong to the line.
I will choose:
(0, 0) and (2, -6)
For the slope, we just take the quotient between:
Δy = -6 - 0 = -6 (the difference in the y-components)
Δx = 2 - 0 = 2 (the difference in the x-components)
the slope is:
k = Δy/Δx = -6/2 = -3
Then the slope is -3, and we can write the equation as:
y = -3*x
Then:
"The equation of the line is y = -3x" is true.
