Write the equation of the line that passes through the points left bracket, minus, 4, comma, 9, right bracket(−4,9) and left bracket, minus, 1, comma, 9, right bracket(−1,9). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
The equation of a line passing through two points (x1, y1) and (x2, y2) can be written in point-slope form as:
y - y1 = m(x - x1)
where m is the slope of the line.
In this case, the points are (-4,9) and (-1,9):
y - 9 = m(x - (-4))
y - 9 = m(x + 4)
Now, to find the slope, we can use the formula:
m = (y2 - y1) / (x2 - x1)
For the given points, we have:
m = (9 - 9) / (-1 - (-4))
m = 0 / 3
m = 0
Since the slope is 0, the line is horizontal.
Therefore, the equation of the line passing through (-4,9) and (-1,9) is:
y - 9 = 0(x + 4)
This can be simplified to:
y - 9 = 0
y = 9