When given two points we can use the point-slope formula to obtain the equation for the line and then convert to the slope-intercept form.
To use the point-slope formula we must first calculate the slope using the two points.
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 two points from the problem gives:
#m = (color(red)(-6) - color(blue)(8))/(color(red)(-4) - color(blue)(-5))#
#m = (color(red)(-6) - color(blue)(8))/(color(red)(-4) + color(blue)(5))#
#m = (-14)/1#
#m = -14#
Now, having obtained the slope we can use the point-slope formula using the slope we have calculated and either of the points.
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 and one of the points gives:
#(y - color(red)(-6)) = color(blue)(-14)(x - color(red)(-4))#
#(y + color(red)(6)) = color(blue)(-14)(x + color(red)(4))#
We can now solve for #y# to put the equation in the slope-intercept form.
#y + color(red)(6) = color(blue)(-14)x + (color(blue)(-14) xx color(red)(4))#
#y + color(red)(6) = color(blue)(-14)x - 56#
#y + color(red)(6) - 6 = color(blue)(-14)x - 56 - 6#
#y + 0 = color(blue)(-14)x - 62#
#y = color(blue)(-14)x - 62#
