Write the equation of the line that passes through the points (-5,9) and (-2,1). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
First, we need to find the slope of the line. The slope is given by the formula:
slope = (y2 - y1) / (x2 - x1)
Using the given points (-5,9) and (-2,1), we have:
x1 = -5
y1 = 9
x2 = -2
y2 = 1
slope = (1 - 9) / (-2 - (-5))
slope = (1 - 9) / (-2 + 5)
slope = (-8) / (3)
slope = -8/3
Now that we have the slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
where m is the slope, (x1, y1) is any point on the line.
Using the first point (-5,9):
y - 9 = (-8/3)(x - (-5))
y - 9 = (-8/3)(x + 5)
Now, let's simplify the equation:
y - 9 = (-8/3)x - (8/3)(5)
y - 9 = (-8/3)x - (8/3)(5)
y - 9 = (-8/3)x - (8/3)(5)
y - 9 = (-8/3)x - 40/3
The equation of the line that passes through the points (-5,9) and (-2,1) in point-slope form is:
y - 9 = (-8/3)x - 40/3