Final answer:
The slope-intercept equation for the line passing through (0, -4) and (4, 1) is y = (5/4)x - 4.
Step-by-step explanation:
The slope-intercept equation, y = mx + b, represents a straight line on a graph. In this equation, m represents the slope and b represents the y-intercept. To find the slope, we use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of two points on the line. Given the points (0, -4) and (4, 1), we can calculate the slope as m = (1 - (-4)) / (4 - 0) = 5 / 4. Plugging the slope (m = 5/4) and one of the given points (0, -4) into the equation y = mx + b, we can solve for the y-intercept: -4 = (5/4)(0) + b. Simplifying this equation gives us b = -4. Therefore, the slope-intercept equation for the line passing through (0, -4) and (4, 1) is y = (5/4)x - 4.