Graph Intersection: Points on the Line y=2(x+2)-1

Through which points does the function below pass?

$y=2(x+2)-1$

To determine through which points the function $y = 2(x+2) - 1$ passes, let's proceed methodically.

Step 1: Simplify the expression of the linear function:

The given function is $y = 2(x+2) - 1$. Distribute the $2$ over the terms inside the parenthesis:
$y = 2x + 4 - 1$

Simplify further by combining like terms:
$y = 2x + 3$

Step 2: Evaluate the function at different $x$-values to find which points lie on the line represented by the function $y = 2x + 3$.

Step 3: Check each of the provided choice points:

• For choice $(0,0)$: Substituting $x = 0$ into $y = 2x + 3$, we get $y = 2(0) + 3 = 3$. This does not match $y = 0$.
• For choice $(10,13)$: Substituting $x = 10$ into $y = 2x + 3$, we get $y = 2(10) + 3 = 23$. This does not match $y = 13$.
• For choice $(5,13)$: Substituting $x = 5$ into $y = 2x + 3$, we get $y = 2(5) + 3 = 13$. This matches $y = 13$, so this point lies on the line.
• For choice $(4,13)$: Substituting $x = 4$ into $y = 2x + 3$, we get $y = 2(4) + 3 = 11$. This does not match $y = 13$.

Therefore, the point through which the given function passes is $(5,13)$.