Question

Which of the following points are on the line 2x + 3y = 8?

1) (0,3)
2) (2,0)
3) (0,2)
4) (3,0)
5) (4,0)
6) (0,2½)
7) (2…", 0)
8) (0.4)
9) (3.2)
10) (2,3)

Answer 1

To find out which points are on the line 2x + 3y = 8, plug in the coordinates for x and y into the equation and see if the equation is true for each point. Points that satisfy the equation lie on the line and thus represent the dependence of y on x in the context of the given linear equation.

Step-by-step explanation:

To determine which of the points are on the line 2x + 3y = 8, each point can be plugged into the equation, replacing x and y with the coordinates from the point, to check if the equation holds true. Here's how we can test one of the points:

1. Take the point (2,0) and plug the x-value (2) and y-value (0) into the equation: 2(2) + 3(0) = 8.
2. After simplifying, we get 4 + 0 = 8, which is not true, so point (2,0) is not on the line.
3. Repeat this process for each point to see which ones satisfy the equation.

This method identifies points that lie on the given line which is essential in subjects like algebra and analytical geometry for understanding the dependence of y on x.