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)(-3))/(color(red)(-2) - color(blue)(1)) = (color(red)(-4) + color(blue)(3))/(color(red)(-2) - color(blue)(1)) = (-1)/-3 = 1/3#
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 substitute the slope and the values for one of the points and solve for #b#:
#-3 = (color(red)(1/3) xx 1) + color(blue)(b)#
#-3 = 1/3 + color(blue)(b)#
#-color(red)(1/3) - 3 = -color(red)(1/3) + 1/3 + color(blue)(b)#
#-color(red)(1/3) - (3/3 xx 3) = 0 + color(blue)(b)#
#-color(red)(1/3) - 9/3 = color(blue)(b)#
#-10/3 = color(blue)(b)#
We can now substitute the slope and #b# value we calculated into the formula giving:
#y = color(red)(1/3)x + color(blue)(-10/3)#
#y = color(red)(1/3)x - color(blue)(10/3)#
