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.
We can substitute the slope and values from the point to give:
#(y - color(red)(1)) = color(blue)(8)(x - color(red)(7))#
We can also transform this equation to the slope-intercept form by solving for #y#. 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)(8) xx x) - (color(blue)(8) xx color(red)(7))#
#y - color(red)(1) = 8x - 56#
#y - color(red)(1) + 1 = 8x - 56 + 1#
#y - 0 = 8x - 55#
#y = color(red)(8)x - color(blue)(55)#
