Final answer:
The slope-intercept form of the equation of the line through the given points (2, -5) and (0, 1) is y = -3x + 1.
Step-by-step explanation:
To write the slope-intercept form of the equation of a line, we need to determine the slope and the y-intercept.
To find the slope, we use the formula: slope = (change in y)/(change in x).
Using the given points (2, -5) and (0, 1), we have:
change in y = -5 - 1 = -6
change in x = 2 - 0 = 2
slope = (-6)/(2) = -3
Next, we can use the formula y = mx + b, where m is the slope and b is the y-intercept, to find the equation of the line.
Using the point (2, -5), we have:
-5 = -3(2) + b
-5 = -6 + b
b = 1
Therefore, the equation of the line is y = -3x + 1.