To first identify the equation we can use the point-slope formula and then translate into the slope-intercept form.

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.

We have been given the slope #color(blue)(m = -1/13)#

We have been given a point on the line #color(red)(((-7, 5)))#

Substituting gives:

#(y - color(red)(5)) = color(blue)(-1/13)(x - color(red)(-7))#

#(y - color(red)(5)) = color(blue)(-1/13)(x + color(red)(7))#

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.

We can solve for #y# to put our equation into this form:

#(y - color(red)(5)) = color(blue)(-1/13)(x + color(red)(7))#

#(y - color(red)(5)) = color(blue)(-1/13)x + (color(blue)(-1/13) * color(red)(7)))#

#y - color(red)(5) = color(blue)(-1/13)x + (color(blue)(-7/13))#

#y - 5 = color(blue)(-1/13)x - 7/13#

#y - 5 + color(red)(5) = color(blue)(-1/13)x - 7/13 + color(red)(5)#

#y - 0 = color(blue)(-1/13)x - 7/13 + (color(red)(5) * 13/13)#

#y = color(blue)(-1/13)x - 7/13 + color(red)(65/13)#

#y = color(blue)(-1/13)x + color(red)(58/13)#