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​ slope-intercept form of the equation of the​ line?
(Simplify your answer. Use integers or fractions for any numbers in the​ equation.)

Answer 1

To find the equation in point-slope form, we start by finding the slope of the line.

The formula for finding the slope, given two points (x1, y1) and (x2, y2), is:

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

Using the given points: (-9, 7) and (9, 1), we can plug in the values into the slope formula:

slope = (1 - 7) / (9 - (-9))
slope = (-6) / (9 + 9)
slope = -6 / 18
slope = -1/3

Now that we have the slope, we can use it to find the equation in point-slope form.
Using the point-slope form equation:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is any point on the line, we can choose either of the given points to plug into the equation. Let's use (-9, 7):

y - 7 = (-1/3)(x - (-9))
y - 7 = (-1/3)(x + 9)
y - 7 = (-1/3)x - 3
y = (-1/3)x - 3 + 7
y = (-1/3)x + 4

Therefore, the equation in slope-intercept form is:

y = (-1/3)x + 4