Write the equation of the line that passes through the points (-3, -8) and (-9, 9). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
The equation of a line in point-slope form is given by y - y1 = m(x - x1), where (x1, y1) are the coordinates of a point on the line and m is the slope of the line.
Let's calculate the slope of the line using the two given points. The slope (m) is given by m = (y2 - y1)/(x2 - x1), where (x2, y2) are the coordinates of the second point and (x1, y1) are the coordinates of the first point.
Using the values (-3, -8) and (-9, 9), we can substitute into the slope formula:
m = (9 - (-8))/(-9 - (-3))
m = (9 + 8)/(-9 + 3)
m = 17/-6
m = -17/6
The slope of the line is -17/6.
Now that we have the slope, we can use either of the given points to form the equation of the line in point-slope form.
Let's use the first point (-3, -8):
y - (-8) = (-17/6)(x - (-3))
y + 8 = (-17/6)(x + 3)
This is the equation of the line in point-slope form.