Question

Write an equation in​ point-slope form of the line that passes through the given​ points.
​(​-9,​7), ​(9​,​1)

Answer 1

To find the equation of the line in point-slope form, we need to determine the slope and one point on the line.

The formula to calculate the slope between two points is:

m = (y2 - y1) / (x2 - x1)

Using the given points (-9, 7) and (9, 1), we can calculate the slope:

m = (1 - 7) / (9 - (-9))
m = -6 / 18
m = -1/3

Now we have the slope, we can use the point-slope form of a line which is:

y - y1 = m(x - x1)

Let's substitute the coordinates of one point in the equation. We'll use the first point (-9, 7):

y - 7 = -1/3(x - (-9))
y - 7 = -1/3(x + 9)

So, the equation in point-slope form of the line that passes through the points (-9, 7) and (9, 1) is:
y - 7 = -1/3(x + 9)