Final Answer:
The slope equation for the given points (-1, -26), (0, -5), (1, 0), (2, -4), (3, 8) is y = 7x - 19.
Step-by-step explanation:
To find the slope equation, we can use the formula for the slope (m) between two points (x₁, y₁) and (x₂, y₂), which is given by (y₂ - y₁) / (x₂ - x₁). Taking consecutive points from the provided set, we can calculate the slopes between each pair.
Starting with the first two points (-1, -26) and (0, -5), the slope is (−5 − (−26)) / (0 − (−1)) = 21. Using the point-slope form of a linear equation (y - y₁ = m(x - x₁)), we can write the equation for this line as y + 26 = 21(x + 1).
Similarly, for the next three pairs of points, we find the slopes and equations:
1. (0, -5) and (1, 0) yield a slope of (0 - (-5)) / (1 - 0) = 5, resulting in the equation y + 5 = 5(x - 0).
2. (1, 0) and (2, -4) give a slope of (-4 - 0) / (2 - 1) = -4, leading to the equation y - 0 = -4(x - 1).
3. (2, -4) and (3, 8) result in a slope of (8 - (-4)) / (3 - 2) = 12, giving the equation y + 4 = 12(x - 2).
By simplifying each of these equations, we find the common slope equation for all the points: y = 7x - 19.