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),(6,2)

Question

What is the​ point-slope form of the equation of the​ line?
  
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Answer 1

To find the equation in point-slope form, we can use the formula:

y - y1 = m(x - x1)

Where (x1, y1) is one of the given points and m is the slope of the line.

Given points: (-9, 7) and (6, 2)

First, we calculate the slope:

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

m = (2 - 7) / (6 - (-9))
m = -5 / 15
m = -1/3

Using the point-slope form equation with the point (-9, 7), we have:

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

To write the equation in slope-intercept form (y = mx + b), we need to solve for y by simplifying the equation:

y - 7 = -1/3x - 3
y = -1/3x - 3 + 7
y = -1/3x + 4

Therefore, the equation in slope-intercept form is y = -1/3x + 4.