Question

x 0 1 2 3 4
y 5 3 1 -1 -3
write the equation that created this table.
y = 4x - 3
y = 2x + 1
y = -2x - 1
y = -2x + 5

Explanation:

Step1: Identify y-intercept (x=0)

When $x=0$, $y=5$. In slope-intercept form $y=mx+b$, $b=5$.

Step2: Calculate slope m

Use points $(0,5)$ and $(1,3)$:
$$m=\frac{y_2-y_1}{x_2-x_1}=\frac{3-5}{1-0}=-2$$

Step3: Verify with other points

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

Answer:

y = -2x + 5