Answer:
(D) The bottom graph, and (A) The top table.
Step-by-step explanation:
The easiest way to pick out the wrong answers is simply through substitution. Substitute the input into the x part of the equation that is given and if it doesn't match up with y everytime, then it is incorrect.
From table A (top table), the input x can be substituted into y = x + 2 which will come out as the output so it is correct.
For table A:
x = -3 → y = x + 2 → y = (-3) + 2 → y = -1 = -1
x = -2 → y = x + 2 → y = (-2) + 2 → y = 0 = 0
x = -1 → y = x + 2 → y = (-1) + 2 → y = 1 = 1
x = 0 → y = x + 2 → y = (0) + 2 → y = 2 = 2
x = 1 → y = x + 2 → y = (1) + 2 → y = 3 = 3
Since the table matches up with the inputs and outputs of the table, it is a correct answer.
For table B:
x = 3 → y = x + 2 → y = (3) + 2 → y = 5 = 5
x = 4 → y = x + 2 → y = (4) + 2 → y = 6 ≠ 7
x = 5 → y = x + 2 → y = (5) + 2 → y = 7 ≠ 9
x = 6 → y = x + 2 → y = (6) + 2 → y = 8 ≠ 11
x = 7 → y = x + 2 → y = (7) + 2 → y = 9 ≠ 13
5 out of the 6 y values of the table do not match the equation, so table B must be incorrect.
Graph C:
Notice how you can see the line cross the x, and y axis. When the line crosses the x axis, it is an x intercept which means y is 0. When the line crosses the y axis, it is a y intercept which means x is 0.
Since the line crosses the y axis at 2, this means that an x of 0 must lead to a y of 2 which it does.
x = 0 → y = x + 2 → y = (0) + 2 → y = 2 = 2.
But the x intercept doesn't match up as shown here.
y = 0 → y = x + 2 → (0) = x + 2 →
0 – 2 = x + 2 – 2 → -2 = x → x = -2 ≠ -1
When graphing the line y = x + 2, it's x intercept should be (-2,0). While on this graph, it's (-1,0). This means that this graph is incorrect which leads to D being another correct answer.
✓ Table A: y = x + 2
× Table B: y = 2x – 1
× Graph C: y = 2x + 2
✓ Graph D: y = x + 2
