If it cuts the x-axis at #4# this is the point #(4, 0)#.
We can now find the slope given 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 values from the points in the problem gives:
#m = (color(red)(0) - color(blue)(4))/(color(red)(4) - color(blue)(2)) = (-4)/2 = -2#
We can now use the point-slope formula to write an equation for the 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 we calculated and the point from the problem gives:
#(y - color(red)(4)) = color(blue)(-2)(x - color(red)(2))#
We can also substitute the slope we calculated and the point we determine from where the 3-axis is cut giving:
#(y - color(red)(0)) = color(blue)(-2)(x - color(red)(4))#
We can also solve this equation for #y# to put the 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)(0) = (color(blue)(-2) xx x) - (color(blue)(-2) xx color(red)(4))#
#y = -2x - (-8)#
#y = color(red)(-2)x + color(blue)(8)#
