Question

x | y
0 | 1
1 | 4
2 | 7
4 | 13
5 | 16
write the equation that created this table.
options:
y = 4x + 3
y = 3x + 4
y = 3x + 1
y = x + 1

Explanation:

Step1: Identify slope (rate of change)

Calculate $\frac{\Delta y}{\Delta x}$ using two points, e.g., $(0,1)$ and $(1,4)$:
$\frac{4-1}{1-0}=3$

Step2: Find y-intercept (x=0)

When $x=0$, $y=1$, so intercept $b=1$.

Step3: Verify with other points

Test $x=2$: $y=3(2)+1=7$, matches the table.
Test $x=4$: $y=3(4)+1=13$, matches the table.
Test $x=5$: $y=3(5)+1=16$, matches the table.

Answer:

C. $y = 3x + 1$