Compare the equations and graphs of lines after vertical shifts in this activity.
[i]Answer these open ended questions on your own or with others to form deeper math connections. [/i]
The equations of two lines are [math]y=\frac{2}{3}x[/math] and [math]y=\frac{2}{3}x-4[/math]. How would the graphs of these lines be the same? How would they be different? What else do you notice? Be specific.[br]
Write the equation of a line with a [math]y[/math]-intercept of [math]\left(0,-12\right)[/math] and a slope of [math]\frac{1}{2}[/math] in slope-intercept form [math]y=mx+b[/math].
[math]y=\frac{1}{2}x-12[/math]
What do you notice about the original and the transformed (new) line?