Question

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

x	y
-1	-2
2	10
5	22
8	34

answer attempt 2 out of 3

Explanation:

Step1: Calculate the slope (m)

The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Let's use the points \((-1, -2)\) and \((2, 10)\).
\( m = \frac{10 - (-2)}{2 - (-1)} = \frac{12}{3} = 4 \)

Step2: Find the y-intercept (b)

Use the slope-intercept form \( y = mx + b \) and substitute \( m = 4 \) and a point, say \((-1, -2)\).
\( -2 = 4(-1) + b \)
\( -2 = -4 + b \)
Add 4 to both sides: \( b = -2 + 4 = 2 \)

Step3: Write the equation

Now that we have \( m = 4 \) and \( b = 2 \), the slope-intercept form is \( y = 4x + 2 \).

Answer:

\( y = 4x + 2 \)