First, we need to determine the slope of the line for the equation. 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)(2))/(color(red)(3) - color(blue)(-1)) = (color(red)(-4) - color(blue)(2))/(color(red)(3) + color(blue)(1)) = -6/4 = -3/2#
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.
Because we have calculated the slope and the problem gives us a point from the line, we can substitute the slope we calculated for #m# and we can substitute the values from either of the points in the problem and solve for #b#:
#2 = (color(red)(-3/2) xx -1) + color(blue)(b)#
#2 = 3/2 + color(blue)(b)#
#-color(red)(3/2) + 2 = -color(red)(3/2) + 3/2 + color(blue)(b)#
#-color(red)(3/2) + (2/2 xx 2) = 0 + color(blue)(b)#
#-color(red)(3/2) + 4/2 = color(blue)(b)#
#1/2 = color(blue)(b)#
We can now substitute the slope and #b# value we calculated into the formula to give the equation in slope-intercept form:
#y = color(red)(-3/2)x + color(blue)(1/2)#
