To write an equation for this line give the slope and one point 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.
Substituting the point and slope from the problem gives:
#(y - color(red)(5)) = color(blue)(-2/5)(x - color(red)(-8))#
#(y - color(red)(5)) = color(blue)(-2/5)(x + color(red)(8))#
Or, we can solve for #y# to put this equation in the more familiar slope-intercept form:
The slope-intercept form of a linear equation is:
#y = color(red)(m)x + color(blue)(b)#
Where #color(red)(m)# is the slope and #color(blue)(b# is the y-intercept value.
#y - color(red)(5) = color(blue)(-2/5)x + (color(blue)(-2/5) xx color(red)(8))#
#y - color(red)(5) = color(blue)(-2/5)x - 16/5#
#y - color(red)(5) + 5 = color(blue)(-2/5)x - 16/5 + 5#
#y - 0 = -2/5x - 16/5 + (5/5 xx 5)#
#y = -2/5x - 16/5 + 25/5#
#y = -2/5x + 9/5#
