1. The problem is to find the linear equation for the sequence with term numbers 0 to 4 and term values -27, -19, -11, -3, 5. 2. The formula for a linear sequence is $y = mx + b$, where $m$ is the slope (common difference) and $b$ is the y-intercept (term value when $x=0$). 3. Calculate the slope $m$ using two points: $m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-19 - (-27)}{1 - 0} = \frac{8}{1} = 8$. 4. The y-intercept $b$ is the term value at $x=0$, which is $-27$. 5. Therefore, the equation of the sequence is $$y = 8x - 27$$. 6. Check with term number 1: $y = 8(1) - 27 = 8 - 27 = -19$, which matches the given value. Final answer: $$y = 8x - 27$$.