Question

find the equation of the linear function represented by the table below in slope-intercept form.

x	y
-1	5
1	3
3	1
5	-1

answer attempt 1 out of 4

Explanation:

Step1: Calculate the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points, say $(-1, 5)$ and $(1, 3)$. Then $m = \frac{3 - 5}{1 - (-1)} = \frac{-2}{2} = -1$.

Step2: Find the y-intercept (b)

Use the slope-intercept form $y = mx + b$. Substitute $m = -1$ and a point, e.g., $(1, 3)$: $3 = -1(1) + b$. Solving for b: $3 = -1 + b \implies b = 4$.

Step3: Write the equation

Substitute $m = -1$ and $b = 4$ into $y = mx + b$: $y = -x + 4$.

Answer:

$y = -x + 4$