Write the equation of the line that passes through the points left bracket, 8, comma, minus, 5, right bracket(8,−5) and left bracket, minus, 6, comma, 5, right bracket(−6,5). Put your answer in fully simplified point-slope form, unless it is a vertical or horizontal line.
To find the equation of the line in point-slope form, we need to find the slope of the line and a point on the line. The formula for slope is given by:
m = (y2 - y1)/(x2 - x1)
Using the points (8, -5) and (-6, 5):
m = (5 - (-5))/(-6 - 8) = 10/-14 = -5/7
Now, we can choose any of the given points to plug into the point-slope form equation. Let's use the point (8, -5):
y - y1 = m(x - x1)
y + 5 = (-5/7)(x - 8)
Expanding:
y + 5 = (-5/7)x + 40/7
Moving terms to one side:
y = (-5/7)x + 40/7 - 5
Simplifying:
y = (-5/7)x + 40/7 - 35/7
y = (-5/7)x + 5/7
Therefore, the equation of the line in point-slope form is y = (-5/7)x + 5/7.