Which set of points includes all of the solutions for y = five halves times x plus three halves?

line going through negative 1 comma negative 1 and 1 comma 4

(x, five halves times x plus three halves) for all real numbers
(−1, −1), (0, 1.5), (1, 4)
(x, y) for all real numbers
(−3, −6), (−2, −3.5), (0, 1.5), (2, 6.5), (3, 9)

Question

Which set of points includes all of the solutions for y = five halves times x plus three halves?

line going through negative 1 comma negative 1 and 1 comma 4

(x, five halves times x plus three halves) for all real numbers
 (−1, −1), (0, 1.5), (1, 4)
 (x, y) for all real numbers
 (−3, −6), (−2, −3.5), (0, 1.5), (2, 6.5), (3, 9)

Mooshroom · Answer

For $$y=\frac{ -3 }{ 2 } x+2$$ the set of points that include all solutions are $$(x,y)$$such that$$y=\frac{ -3 }{ 2 }x+2$$; then we have$$(x,y)=(x,\frac{ -3 }{ 2 }x+2)$$.

What is important to stress here is that$$(x,-\frac{3}{2}x+2)$$represents all of the solutions, while other points that we are given represent one solution  (for example, point (2,-1) is just one solution)

Mooshroom · Answer

@mooshroom wrote:

For $$y=\frac{ -3 }{ 2 } x+2$$ the set of points that include all solutions are $$(x,y)$$such that$$y=\frac{ -3 }{ 2 }x+2$$; then we have$$(x,y)=(x,\frac{ -3 }{ 2 }x+2)$$. What is important to stress here is that$$(x,-\frac{3}{2}x+2)$$represents all of the solutions, while other points that we are given represent one solution (for example, point (2,-1) is just one solution)

does this help?