he point-slope formula can be used to find the equation. First we must determine the slope. 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)(-4))/(color(red)(2) - color(blue)(-2))#
#m = (color(red)(4) + color(blue)(4))/(color(red)(2) + color(blue)(2)) = 8/4 = 2#
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 first point gives:
#(y - color(red)(-4)) = color(blue)(2)(x - color(red)(-2))#
#(y + color(red)(4)) = color(blue)(2)(x + color(red)(2))#
We can also substitute the slope we calculated and the second point giving:
#(y - color(red)(4)) = color(blue)(2)(x - color(red)(2))#
We can also solve this equation for #y# to put the equation in the familiar 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)(4) = (color(blue)(2) xx x) - (color(blue)(2) xx color(red)(2))#
#y - color(red)(4) = 2x - 4#
#y - color(red)(4) + 4 = 2x - 4 + 4#
#y - 0 = 2x - 0#
#y = 2x#
