Answer:
y = x + 3
Explanation:
To know which of the equations represent the relationship between x and y, you need to substitute the x and y values into the equation. If when the equation is solved, the left-hand and right-hand side of the equation equal each other and hence the equation is true, then the equation must be correct in expressing the relationship between the x and y values. If not, then it is not correct.
As this question is only dealing with linear equations, we know that the gradient of the line is constant and hence the rate of change in x and y values is constant. Therefore, we can choose to substitute any of the given combinations of x and y values into the equation to obtain the correct equation. As it is easier to use smaller numbers for smaller calculations, we'll use the first combination of x = 1 and y = 4 .
Equation No. 1 : y = 3x + 1 where x = 1 , y = 4 and x = 2 , y = 5
( 4 ) = 3 ( 1 ) + 1
4 = 4
However, as this equation has a constant not equal to 1 in front of the x variable and hence a different gradient to the other equations, we will substitute the second combination of x and y values.
( 5 ) = 3 ( 2 ) + 1
5 = 6
Therefore, equation is false / incorrect.
Equation No. 2 : y = x + 1 where x = 1 , y = 4
( 4 ) = ( 1 ) + 1
4 = 2
Therefore, equation is false / incorrect.
Equation No. 3 : y = x + 3 where x = 1 , y = 4
( 4 ) = ( 1 ) + 3
4 = 4
Therefore, equation is true / correct.
Equation No. 4 : y = x - 3 where x = 1 , y = 4
( 4 ) = ( 1 ) - 3
4 = - 2
Therefore, equation is false / incorrect.