Question

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

$$\begin{tabular}{|c|c|} \\hline $x$ & $y$ \\\\ \\hline $-1$ & $2$ \\\\ \\hline $1$ & $6$ \\\\ \\hline $3$ & $10$ \\\\ \\hline $5$ & $14$ \\\\ \\hline \\end{tabular}$$

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 \((1, 6)\).
\( m = \frac{6 - 2}{1 - (-1)} = \frac{4}{2} = 2 \).

Step2: Find the y-intercept (b)

The slope-intercept form is \( y = mx + b \). We know \( m = 2 \), and we can use the point \((-1, 2)\) to solve for \( b \).
Substitute \( x = -1 \), \( y = 2 \), and \( m = 2 \) into the equation:
\( 2 = 2(-1) + b \)
\( 2 = -2 + b \)
Add 2 to both sides: \( b = 4 \).

Step3: Write the equation

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

Answer:

\( y = 2x + 4 \)