Linear Parent Graph and Transformations

Students learn that the linear equation y = x, or the diagonal line that passes through the origin, is called the parent graph for the family of linear equations. Students also learn the different types of transformations of the linear parent graph. For example, if the parent graph is shifted up or down (y = x + 3), the transformation is called a translation. If the parent graph is made steeper or less steep (y = 5 x), the transformation is called a dilation. And if the parent graph is changed so that it falls to the right instead of rising to the right (y = -x), the transformation is called a reflection.