Which function has the same y-intercept as the function y=2 /3x-3? A 2/3 x + 3y = -3B -2/3 x + 3y = 6C x + 4y = 12D 6x - 7y = 21 PLEAZ answer im in a hurry

Accepted Solution

Answer:Option D.Step-by-step explanation:The given function is[tex]y=\frac{2}{3}x-3[/tex]Substitute x=0 in the given function to find the y-intercept.[tex]y=\frac{2}{3}(0)-3=-3[/tex]The y-intercept of the given function is -3. We need to find the equation whose y-intercept is -3.Substitute x=0 in the given each of the equations to find the y-intercepts of those equation.First equation is[tex]\frac{2}{3}x+3y=-3[/tex][tex]\frac{2}{3}(0)+3y=-3[/tex][tex]3y=-3[/tex][tex]y=-1[/tex]y-intercept is -1.Second equation is[tex]-\frac{2}{3}x+3y=6[/tex][tex]-\frac{2}{3}(0)+3y=6[/tex][tex]3y=6[/tex][tex]y=2[/tex]y-intercept is 2.Third equation is[tex]x+4y=12[/tex][tex](0)+4y=12[/tex][tex]4y=12[/tex][tex]y=3[/tex]y-intercept is 3.Fourth equation is[tex]6x-7y=21[/tex][tex]6(0)-7y=21[/tex][tex]-7y=21[/tex][tex]y=-3[/tex]y-intercept is -3.Therefore, the correct option is D.