Write the equation of the line that passes through the points (-8,5) and (9,-5). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
To find the equation of the line that passes through the points (-8,5) and (9,-5), we need to find the slope of the line.
The slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the points (-8,5) and (9,-5), we can substitute the coordinates into the formula:
m = (-5 - 5) / (9 - (-8))
m = (-10) / (9 + 8)
m = (-10) / 17
Now that we have the slope (m), we can use the point-slope form of the equation:
y - y1 = m(x - x1)
Using the first point (-8,5), we can substitute the values into the equation:
y - 5 = (-10 / 17)(x - (-8))
y - 5 = (-10 / 17)(x + 8)
Simplifying the equation gives us:
y - 5 = (-10 / 17)(x + 8)
y - 5 = (-10 / 17)x + (-10 / 17)(8)
y - 5 = (-10 / 17)x - 80 / 17
Thus, the equation of the line that passes through the points (-8,5) and (9,-5) is:
y - 5 = (-10 / 17)x - 80 / 17