First we must 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)(1) - color(blue)(3))/(color(red)(-3) - color(blue)(-1)) = (color(red)(1) - color(blue)(3))/(color(red)(-3) + color(blue)(1)) = (-2)/(-2) = 1#
We can now use the point-slope formula to write an equation for the line. 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 slope we calculated and the values from the first point in the problem gives:
#(y - color(red)(3)) = color(blue)(1)(x - color(red)(-1))#
#(y - color(red)(3)) = color(blue)(1)(x + color(red)(1))#
#(y - color(red)(3)) = (x + color(red)(1))#
We can now solve for #y# to put the equation in 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)(3) = x + color(red)(1)#
#y - color(red)(3) + 3 = x + color(red)(1) + 3#
#y - 0 = x + 4#
#y = x + color(blue)(4)#
Or
#y = color(red)(1)x + color(blue)(4)#
