Questions: Write the linear equation that gives the rule for this table. x y 3 29 4 13 5 -3 6 -19 Write your answer as an equation with y first, followed by an equals sign.

Write the linear equation that gives the rule for this table.

x y
3 29
4 13
5 -3
6 -19

Write your answer as an equation with y first, followed by an equals sign.

Transcript text: Write the linear equation that gives the rule for this table. \begin{tabular}{|c|c|} \hline$x$ & $y$ \\ \hline 3 & 29 \\ \hline 4 & 13 \\ \hline 5 & -3 \\ \hline 6 & -19 \\ \hline \end{tabular} Write your answer as an equation with y first, followed by an equals sign.

Solution

Solution Steps

Step 1: Calculate the Slope (m)

To find the slope (m) of the line, we use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substituting the given points $(3, 29)$ and $(4, 13)$, we get $m = \frac{13 - 29}{4 - 3} = -16$.

Step 2: Calculate the Y-intercept (b)

Using the slope $m = -16$ and one of the points, say $(3, 29)$, we can find the y-intercept (b) using the formula $b = y - mx$. Substituting the values, we get $b = 29 - (-16)(3) = 77$.