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)(-2) - color(blue)(-1))/(color(red)(2) - color(blue)(1)) = (color(red)(-2) + color(blue)(1))/(color(red)(2) - color(blue)(1)) = -1/1#
Next we can use the point-slope formula to find 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.
We can substitute the slope we calculated and the values from the first point in the problem to give:
#(y - color(red)(-1)) = color(blue)(-1)(x - color(red)(1))#
#(y + color(red)(1)) = color(blue)(-1)(x - color(red)(1))#
We can now solve for #y# to convert this equation to 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)(1) = (color(blue)(-1) xx x) - (color(blue)(-1) xx color(red)(1))#
#y + color(red)(1) = -1x - (-1)#
#y + color(red)(1) = -1x + 1#
#y + color(red)(1) - 1 = -1x + 1 - 1#
#y + 0 = -1x + 0#
#y = color(red)(-1)x + color(blue)(0)#
