What is the equation of the line that is parallel to the given line and has an x-intercept of –3? y = Two-thirdsx + 3 y = Two-thirdsx + 2 y = Negative three-halvesx + 3 y = –Three-halvesx + 2

Accepted Solution

Answer:[tex]y=\frac{2}{3} x+2[/tex]Step-by-step explanation:Equation [tex]y=\frac{2}{3} x+3[/tex] is parallel to [tex]y=\frac{2}{3} x+2[/tex], as they share the same slope of x and the ony difference between them is that the first one has the intercept of y = 3 and the second equation has the intercept of y =2.In the equation [tex]y=\frac{2}{3} x+2[/tex], when y= 0 we can find the intercept of x (which is the value that takes x when y=0=, [tex]y=0=\frac{2}{3} x+2[/tex] . by subtracting 2 in the two terms ⇒ [tex]\frac{2}{3} x=-2[/tex] .  Then, multiplying boths sides by (3/2) ⇒[tex]x=(-2)\frac{3}{2} =(-3)[/tex].Finally, x intercept equals (-3), and both curves are parallel (see the picture attached).