Which graph represents a function with direct variation? A coordinate plane with a line passing through (negative 4, 0) and (0, negative 2). A coordinate plane with a line passing through (negative 5, 4) and (0, 3). A coordinate plane with a line passing through (negative 4, negative 6) and (0, 3). A coordinate plane with a line passing through (negative 1, negative 4), (0, 0) and (1, 4).

Answer:A line passing through the points (-1,-4),(0,0) and (1,4)Step-by-step explanation:we know thatA relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex] 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 casePart 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 originFind out the value of k[tex]k=y/x[/tex]For the point (-1,-4)substitute[tex]k=-4/-1=4[/tex]For the point (1,4)substitute[tex]k=4/1=4[/tex]The linear equation is  [tex]y=4x[/tex] This line represent a direct variation