Question

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

x	1	2	3	4
y	-1	-6	-11	-16

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 from the table, say \((1, -1)\) and \((2, -6)\).
\( m = \frac{-6 - (-1)}{2 - 1} = \frac{-6 + 1}{1} = -5 \)

Step2: Find the y-intercept (b)

The slope-intercept form is \( y = mx + b \). We can use one of the points, for example, \((1, -1)\) and the slope \( m = -5 \).
Substitute \( x = 1 \), \( y = -1 \), and \( m = -5 \) into the equation:
\( -1 = -5(1) + b \)
\( -1 = -5 + b \)
Add 5 to both sides: \( b = -1 + 5 = 4 \)

Step3: Write the equation

Now that we have \( m = -5 \) and \( b = 4 \), the slope-intercept form is \( y = -5x + 4 \)

Answer:

\( y = -5x + 4 \)