Select all statements that are true about the linear equation.

y=−2x+4

a. the equation 2x+y=4 is represented by the same graph.

b. the graph of the equation is the set of points that are solutions to the equation.

c. the graph of the equation is the set of all points on the coordinate plane.

d. the point (1, 2) lies on the the graph of the equation.

e. the point (0, 2) lies on the graph of the equation.

A. True

In the equation 2x+y=4, subtracting 2x to both sides, we get y=-2x+4

B. True

The graph of equation y=-2x+4 is composed of all the solutions (x, y) of the equation.

C. Wrong

The graph of the equation is only one line, whereas the set of all points on the coordinate plane means the whole plane.

D. True

Substituting (x, y) with (1, 2) in y=-2x+4, we have 2=-2*1+4, which is true.
Thus the point (1, 2) is a solution of the equation, so it is a point on the graph of the equation.

E. False

Substituting x with 0 in -2x+4, the expression becomes 4, which is not equal to 2. So this point is not a solution, therefore it is not on the graph.

A, B, and D are true

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