Final answer:
The equation of the line in slope-intercept form is y = x - 6.
Step-by-step explanation:
The slope-intercept form of the equation of a line is given by y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we can use the formula: m = (y2 - y1) / (x2 - x1). Given the points (-1, -7) and (7, 1),
we can substitute the coordinates into the formula to find the slope: m = (1 - (-7)) / (7 - (-1))
= 8 / 8
= 1.
Since we have the slope, we can choose any of the given points and substitute its coordinates into the equation to find the y-intercept. Let's use the point (-1, -7): -7 = 1(-1) + b.
Solving for b, we get b = -6.
Therefore, the equation of the line in slope-intercept form is y = x - 6.