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​ slope-intercept form of the equation of the​ line?

Answer 1

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

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

Let's label the given points as (x1, y1) = (-9, 7) and (x2, y2) = (6, 2):

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

Now that we have the slope (m = -1/3), we can use the point-slope form of a linear equation to find the equation in point-slope form:

y - y1 = m(x - x1)
y - 7 = (-1/3)(x - (-9))
y - 7 = (-1/3)(x + 9)
3(y - 7) = -1(x + 9)
3y - 21 = -x - 9
x + 3y = -12

To convert the equation to slope-intercept form (y = mx + b), we need to isolate y:

x + 3y = -12
3y = -x - 12
y = (-1/3)x - 4

Therefore, the slope-intercept form of the equation of the line is y = (-1/3)x - 4.