To find the equation for this line we can use the point-slope formula:

The point-slope formula states: #(y - color(red)(y_1)) = color(blue)(m)(x - color(red)(x_1))#

Where #color(blue)(m)# is the slope and #color(red)(((x_1, y_1)))# is a point the line passes through.

In this problem we have been given the slope #color(blue)(m = -7)#

We have also been given a point on the line #color(red)(((2, -8)))#

Substituting these into the formula gives:

#(y - color(red)(-8)) = color(blue)(-7)(x - color(red)(2))#

#y + color(red)(8) = color(blue)(-7)(x - color(red)(2))#

If we want to put this into slope-intercept form we can solve for #y#.

The slope-intercept form of a linear equation is:

#y = color(blue)(m)x + color(red)(b)#

Where #color(blue)(m)# is the slope and #color(red)(b# is the y-intercept value.

#y + color(red)(8) = color(blue)(-7)x + (color(blue)(-7) * color(red)(-2))#

#y + color(red)(8) = color(blue)(-7)x + color(red)(14)#

#y + color(red)(8) - color(green)(8) = color(blue)(-7)x + color(red)(14) - color(green)(8)#

#y + 0 = color(blue)(-7)x + color(red)(6)#

#y = color(blue)(-7)x + color(red)(6)#