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)(1) - color(blue)(3))/(color(red)(-4) - color(blue)(-2)) = (color(red)(1) - color(blue)(3))/(color(red)(-4) + color(blue)(2)) = (-2)/-2 = 1#
Now, 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.
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)(-2))#
#(y - color(red)(3)) = color(blue)(1)(x + color(red)(2))#
We can now solve for #y# to put the equation in slope-intercept form:
#y - color(red)(3) = x + 2#
#y - color(red)(3) + 3 = x + 2 + 3#
#y = x + 5#
