To find the equation of the line through the points (-5, -1) and (3, -3) in terms of x, you can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Where (x1, y1) are the coordinates of one point on the line, and m is the slope of the line.
Given the points (-5, -1) and (3, -3):
(x1, y1) = (-5, -1)
(x2, y2) = (3, -3)
Calculate the slope (m):
m = (y2 - y1) / (x2 - x1)
m = (-3 - (-1)) / (3 - (-5))
m = (-2) / 8
m = -1/4
Now, use the point-slope form with one of the points (let's use (-5, -1)):
y - (-1) = -1/4 * (x - (-5))
y + 1 = -1/4 * (x + 5)
Distribute the slope:
y + 1 = -1/4x - 5/4
Subtract 1 from both sides:
y = -1/4x - 5/4 - 1
y = -1/4x - 9/4
So, the equation of the line in terms of x is y = -1/4x - 9/4.