First, using the information in the problem write the equation in point-slope form. 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 information from the problem gives:
#(y - color(red)(-1)) = color(blue)(4)(x - color(red)(-1))#
#(y + color(red)(1)) = color(blue)(4)(x + color(red)(1))#
Now, we solve for #y# to transform the 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)(4)(x + color(red)(1))#
#y + color(red)(1) = (color(blue)(4) xx x) + (color(blue)(4) xx color(red)(1))#
#y + color(red)(1) = 4x + 4#
#y + color(red)(1) - 1 = 4x + 4 - 1#
#y + 0 = 4x + 3#
#y = color(red)(4)x + color(blue)(3)#
