We can use the point-slope formula to find an equation for the line described in the problem. 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 values from the point in the problem gives:
#(y - color(red)(2)) = color(blue)(4)(x - color(red)(8))#
We can solve this equation 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)(2) = color(blue)(4)(x - color(red)(8))#
#y - color(red)(2) = (color(blue)(4) * x) - (color(blue)(4) * color(red)(8))#
#y - color(red)(2) = 4x - 32#
#y - color(red)(2) + 2 = 4x - 32 + 2#
#y - 0 = 4x - 30#
#y = color(red)(4)x - color(blue)(30)#
