Final answer:
Out of the given points, (4,5), (8,0), and (0,10) lie on the line represented by the equation 5x+4y=40.
Step-by-step explanation:
The question asks to select all points that lie on the graph of the linear equation 5x+4y=40. To check if a point lies on the graph, we substitute the x and y values of the point into the equation and see if the equation holds true. Let's test each option:
- (4,5): 5(4) + 4(5) = 20 + 20 = 40, so this point is on the line.
- (10,0): 5(10) + 4(0) = 50 + 0 = 50, which does not equal 40, so this point is not on the line.
- (8,0): 5(8) + 4(0) = 40 + 0 = 40, so this point is on the line.
- (2,4): 5(2) + 4(4) = 10 + 16 = 26, which does not equal 40, so this point is not on the line.
- (0,8): 5(0) + 4(8) = 0 + 32 = 32, which does not equal 40, so this point is not on the line.
- (0,10): 5(0) + 4(10) = 0 + 40 = 40, so this point is on the line.
Therefore, the points that are on the graph of the line 5x+4y=40 are (4,5), (8,0), and (0,10).