Final answer:
To find the point-slope form for the line passing through (-8,-6) and (4,-3), calculate the slope as 1/4 and then use the first point with the slope in the point-slope equation, resulting in y + 6 = 1/4(x + 8).
Step-by-step explanation:
To write the equation of the line in point-slope form that passes through the points (-8,-6) and (4,-3), we must first calculate the slope (m) using the given points. The slope is determined by the formula Δy / Δx or (y2 - y1) / (x2 - x1). Using our points (-8,-6) (x1,y1) and (4,-3) (x2,y2), we calculate the slope as:
m = (-3 - (-6)) / (4 - (-8)) = 3 / 12 = 1 / 4.
Now that we have the slope, we can use the point-slope form of the equation, which is y - y1 = m(x - x1). Using the first point (-8,-6) and the slope 1/4, our equation in point-slope form is:
y - (-6) = 1/4(x - (-8)),
which simplifies to:
y + 6 = 1/4(x + 8).