Write an equation in​ point-slope form of the line that passes through the given​ points, then write the equation in​ slope-intercept form.

Question

​(​-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.)

Answer 1

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.