Final answer:
To find the equation of the line through (-12,-5) and (0,-9), calculate the slope (-4/12 which simplifies to -1/3), then use the point-slope form with either point to get y = -1/3x - 1 as the final equation.
Step-by-step explanation:
To find the equation of the line that passes through the points (-12,-5) and (0,-9), we first need to calculate the slope of the line (m), which is the change in y divided by the change in x. The formula for slope is m = (y2 - y1) / (x2 - x1).
Using our points (-12,-5) and (0,-9):
m = (-9 - (-5)) / (0 - (-12)) = (-9 + 5) / (0 + 12) = -4 / 12 = -1/3
With the slope, we can use the point-slope form to find the equation of the line. The point-slope formula is y - y1 = m(x - x1). Using the slope and one of the points, let's say (-12, -5), we get the equation:
y - (-5) = -1/3(x - (-12))
Simplify this to obtain the slope-intercept form, y = mx + b:
y = -1/3x - 1, which is our final equation for the line.