Final answer:
To find the equation of the line passing through (-4,6) and (-5,-7), first calculate the slope (13), then use the point-slope formula and rearrange to get the standard form: -13x + y = 58.
Step-by-step explanation:
To find an equation of the line passing through the pair of points (-4,6) and (-5,-7), the first step is to calculate the slope (m) of the line. The slope is determined by the difference in y-values divided by the difference in x-values:
m = (y2 - y1)/(x2 - x1) = (-7 - 6)/(-5 + 4) = -13/-1 = 13.
Using the slope and one of the points, say (-4,6), we can use the point-slope form of the line equation to create the equation:
y - y1 = m(x - x1)
y - 6 = 13(x + 4)
From here, we expand and rearrange to get the equation into the Ax + By = C form:
y - 6 = 13x + 52
Subtract y from both sides and add 6:
-13x + y = 58
This is the desired equation of the line in standard form.