We can use the point slope formula to write an equation for this 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 and the values from the point from the problem gives:
#(y - color(red)(3)) = color(blue)(2)(x - color(red)(-4))#
Solution 1: #(y - color(red)(3)) = color(blue)(2)(x + color(red)(4))#
We can also solve for #y# to put this equation in 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)(3) = (color(blue)(2) xx x) + (color(blue)(2) xx color(red)(4))#
#y - color(red)(3) = 2x + 8#
#y - color(red)(3) + 3 = 2x + 8 + 3#
#y - 0 = 2x + 11#
Solution 2: #y = color(red)(2)x + color(blue)(11)#
