Answer:
Answer:
A line passing through the points (-1,-4),(0,0) and (1,4)
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form y/x=ky/x=k or y=kxy=kx
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
Verify each case
Part 1) A line passing through the points (-4,0) and (0,-2)
This line not represent a direct variation, because the line not passes through the origin.
Part 2) A line passing through the points (-5,4) and (0,3)
This line not represent a direct variation, because the line not passes through the origin.
Part 3) A line passing through the points (-4,-6) and (0,3)
This line not represent a direct variation, because the line not passes through the origin.
Part 4) A line passing through the points (-1,-4),(0,0) and (1,4)
The line passes through the origin
Find out the value of k
k=y/xk=y/x
For the point (-1,-4)
substitute
k=-4/-1=4k=−4/−1=4
For the point (1,4)
substitute
k=4/1=4k=4/1=4
The linear equation is y=4xy=4x
This line represent a direct variation
