Question

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

x	0	1	2	3	4
y	-9	-5	-1	3	7

Explanation:

Step1: Find the slope (m)

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. Let's take two points from the table, say (0, -9) and (1, -5). Then $m = \frac{-5 - (-9)}{1 - 0} = \frac{4}{1} = 4$.

Step2: Find the y-intercept (b)

The slope-intercept form is $y = mx + b$. We know $m = 4$ and we can use the point (0, -9) (when x = 0, y = -9). Substituting into the formula: $-9 = 4(0) + b$, so $b = -9$.

Step3: Write the equation

Using $m = 4$ and $b = -9$ in $y = mx + b$, we get $y = 4x - 9$.

Answer:

$y = 4x - 9$