If it cuts the x-axis at 44 this is the point (4, 0)(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))m=y2−y1x2−x1
Where mm is the slope and (color(blue)(x_1, y_1)x1,y1) and (color(red)(x_2, y_2)x2,y2) 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 = -2m=0−44−2=−42=−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))(y−y1)=m(x−x1)
Where color(blue)(m)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)
