First, we need to determine the slope of the line. The slope can be found by using the formula: #m = (color(red)(y_2) - color(blue)(y_1))/(color(red)(x_2) - color(blue)(x_1))#
Where #m# is the slope and (#color(blue)(x_1, y_1)#) and (#color(red)(x_2, y_2)#) are the two points on the line.
Substituting the values from the points in the problem gives:
#m = (color(red)(-4) - color(blue)(0))/(color(red)(8) - color(blue)(-5)) = (color(red)(-4) - color(blue)(0))/(color(red)(8) + color(blue)(5)) = -4/13#
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.
We can solve for #color(blue)(b)# by substituting the slope we just calculated and one of the points in the problem for #x# and #y#:
#0 = (color(red)(-4/13) * -5) + color(blue)(b)#
#0 = 20/13 + color(blue)(b)#
#0 - 20/13 = 20/13 - 20/13 + color(blue)(b)#
#-20/13 = 0 + color(blue)(b)#
#-20/13 = color(blue)(b)
We can substitute the slope we calculated and the value of #color(red)(b)# we calculated into the formula to write the equation of the line.
#y = color(red)(-4/13)x + color(blue)(-20/13)#
#y = color(red)(-4/13)x - color(blue)(20/13)#
