Question

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

x	1	3	5	7
y	5	13	21	29

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 \((3, 13)\).
\( m = \frac{13 - 5}{3 - 1} = \frac{8}{2} = 4 \)

Step2: Find the y-intercept (b)

Use the slope-intercept form \( y = mx + b \) and substitute \( x = 1 \), \( y = 5 \), and \( m = 4 \).
\( 5 = 4(1) + b \)
\( 5 = 4 + b \)
Subtract 4 from both sides: \( b = 5 - 4 = 1 \)

Step3: Write the equation

Now that we have \( m = 4 \) and \( b = 1 \), the slope-intercept form is \( y = 4x + 1 \).

Answer:

\( y = 4x + 1 \)