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)#
