Final answer:
To determine the slope-intercept equation of the line through (1, -2) and (4, 4), calculate the slope as 2 and solve for the y-intercept to get y = 2x - 4.
Step-by-step explanation:
The subject of the question is to find the slope-intercept equation of the line that passes through the points (1, −2) and (4, 4). First, we calculate the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1), which in this case gives us m = (4 - (-2)) / (4 - 1) = 6 / 3 = 2. Now that we have the slope, we use one of the points and the slope to solve for the y-intercept (b) in the equation y = mx + b. Using the point (1, −2), we get −2 = 2(1) + b, which simplifies to b = −4.
Thus, the slope-intercept equation of the line is y = 2x - 4.