Question

match the equation with the correct graph!
$f(x) = x + 1$

Explanation:

Step1: Identify slope-intercept form

The function $f(x) = x + 1$ follows the slope-intercept form $y = mx + b$, where $m=1$ (slope) and $b=1$ (y-intercept).

Step2: Find y-intercept point

The y-intercept is when $x=0$, so $y = 0 + 1 = 1$. The point is $(0, 1)$.

Step3: Find x-intercept point

The x-intercept is when $y=0$:
$0 = x + 1$
$x = -1$
The point is $(-1, 0)$.

Step4: Verify with second point

Take $x=2$: $y = 2 + 1 = 3$, so the point $(2, 3)$ is on the line.

Step5: Match to correct graph

The first graph has points including $(0, -1)$ (incorrect y-intercept). The second graph has a y-intercept at $(0,1)$, x-intercept at $(-1,0)$, and includes $(2,3)$, which matches the function.

Answer:

The correct graph is the lower (second) one, with y-intercept at $(0,1)$ and x-intercept at $(-1,0)$.