Final answer:
The equation of the line is y - 1 = (-7/2)x - 21/2.
Step-by-step explanation:
To find the equation of the line that passes through the points (-3, 1) and (-5, 8) in point-slope form, we can use the formula:
y - y1 = m(x - x1)
where (x1, y1) is one of the given points on the line, and m is the slope of the line. First, let's find the slope:
m = (y2 - y1) / (x2 - x1) = (8 - 1) / (-5 - (-3)) = 7 / -2 = -7/2
Now, substitute the values of one of the points and the slope into the formula to get the equation:
y - 1 = (-7/2)(x - (-3))
Simplifying further:
y - 1 = (-7/2)(x + 3)
Finally, we can fully reduce the equation by distributing the slope:
y - 1 = (-7/2)x - 21/2
So, the equation of the line that passes through the points (-3, 1) and (-5, 8) in fully reduced point-slope form is y - 1 = (-7/2)x - 21/2.