Question

write the equation that represents the linear relationship between the x-values and y-values in the table.

x	y
-1	-11
1	-1
3	9
5	19

Explanation:

Step1: Find the slope (m)

The slope formula is \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Let's use the points \((-1, -11)\) and \((1, -1)\).
\( m = \frac{-1 - (-11)}{1 - (-1)} = \frac{-1 + 11}{1 + 1} = \frac{10}{2} = 5 \)

Step2: Use point - slope form to find the equation

The point - slope form is \( y - y_1 = m(x - x_1) \). Let's use the point \((1, -1)\) and \( m = 5 \).
\( y - (-1)=5(x - 1) \)
\( y + 1 = 5x-5 \)

Step3: Simplify to slope - intercept form (\(y=mx + b\))

Subtract 1 from both sides: \( y=5x-5 - 1 \), so \( y = 5x-6 \)

We can check with other points. For \(x = 3\), \(y=5\times3-6=15 - 6 = 9\) (which matches the table). For \(x = 5\), \(y=5\times5-6=25 - 6 = 19\) (which also matches the table).

Answer:

\(y = 5x-6\)