Write an equation in point-slope form of the line that passes through the given points, then write the equation in slope-intercept form.
(-9,7), (9,1)
What is the point-slope form of the equation of the line?
(Simplify your answer. Use integers or fractions for any numbers in the equation.)
The point-slope form of the equation of a line is given by:
y - y1 = m(x - x1)
Where (x1, y1) is a point on the line and m is the slope of the line.
Using the given points (-9, 7) and (9, 1), we can calculate the slope:
m = (y2 - y1)/(x2 - x1)
m = (1 - 7)/(9 - (-9))
m = (-6)/(9 + 9)
m = -6/18
m = -1/3
Now we can substitute one of the points and the slope into the point-slope form to get the equation:
y - 7 = (-1/3)(x - (-9))
y - 7 = (-1/3)(x + 9)
Expanding the equation:
y - 7 = (-1/3)x - 3
y = (-1/3)x - 3 + 7
y = (-1/3)x + 4
Therefore, the equation in point-slope form is y = (-1/3)x + 4.