Question

Find an ordered pair (x, y) that is a solution to the equation. 4x + y = 5

Answer 1

Answer:   (0,5)

Another point is (1,1)

There are infinitely many to choose from

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Explanation:

Pick any x value that you want. I'll pick x = 0

4x+y = 5

4(0)+y = 5

0+y = 5

y = 5

So (0,5) is one point on the line.

If we picked x = 1, then,

4x+y = 5

4(1)+y = 5

4+y = 5

y = 5-4

y = 1

So (1,1) is another point on the line.

There are infinitely many points on the line because we can pick infinitely many x values. We can pick any real number for x.

Each (x,y) point is of the form (x, -4x+5) because solving for y gets us y = -4x+5.

The slope of y = -4x+5 is -4, which means that each time x goes up by 1, y drops by 4, or vice versa.