Which equation represents a proportional relationship between the x and y values?A) y = 2 B) y = 14x + 1 C) y = x − 4 D) y = −2x

Answer:D) [tex]y=-2x[/tex]Step-by-step explanation:A linear relationship is of the form [tex]y=mx+b[/tex], where, [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept (constant). For a proportional relationship, the value of [tex]b=0[/tex] and thus it is of the form [tex]y=mx[/tex] Let us check each option and express it in the form above. Option A: [tex]y=2[/tex]This can be written as [tex]y=0x+2[/tex]. So, [tex]b\ne 0[/tex].Since, b \ne 0, therefore, it is not a proportional relationship. Option B: [tex]y=14x+1[/tex] Here, [tex]b=1[/tex]. So, [tex]b\ne 0[/tex].Since, b \ne 0, therefore, it is not a proportional relationship.  Option C: [tex]y=x-4[/tex] Here, [tex]b=-4[/tex]. So, [tex]b\ne 0[/tex].Since, b \ne 0, therefore, it is not a proportional relationship.  Option D: [tex]y=-2x[/tex]This can be rewritten as [tex]y=-2x+0[/tex]There is no y-intercept on this. So, [tex]b=0[/tex] Since,[tex] b = 0[/tex], therefore, it is a proportional relationship. Therefore, the correct option is D.