Write the equation of the line that passes through the points left bracket, minus, 8, comma, 7, right bracket(−8,7) and left bracket, 2, comma, minus, 7, right bracket(2,−7). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
To find the equation of the line passing through the points (-8,7) and (2,-7), we need to find the slope of the line first.
The formula to find the slope (m) of a line passing through two points (x1,y1) and (x2,y2) is given by:
m = (y2 - y1) / (x2 - x1)
Substituting the given points, we get:
m = (-7 - 7) / (2 - (-8))
m = (-14) / (2 + 8)
m = -14/10
m = -7/5
Now, we can use the point-slope form of the equation of a line, where the slope is m and a point on the line is (x1, y1):
y - y1 = m(x - x1)
Choosing the point (-8,7) as the point on the line, we substitute the values:
y - 7 = (-7/5)(x - (-8))
Simplifying and fully simplifying, we get:
5y - 35 = -7x - 56
5y = -7x - 21
y = (-7/5)x - 21/5
Therefore, the equation of the line passing through the points (-8,7) and (2,-7) is y = (-7/5)x - 21/5 in fully simplified point-slope form.