Final answer:
The equation of the line passing through the points (2,4) and (7,-1) in slope-intercept form is y = -x + 6.
Step-by-step explanation:
To write the equation of a line in slope-intercept form, we need to find the slope and the y-intercept.
The slope of a line passing through the points (2,4) and (7,-1) can be found using the formula:
slope = (y2 - y1) / (x2 - x1).
Substituting the values, we get: slope = (-1 - 4) / (7 - 2)
= -5 / 5
= -1.
The y-intercept (b) can be found using the equation: y = mx + b.
Substituting one of the points, (2,4), and the slope, -1, we get:
4 = -1 * 2 + b.
Solving for b, we get: b = 6.
Therefore, the equation of the line in slope-intercept form is y = -x + 6.