In this exploration you will be exploring the relationship between the equations of dilated lines. We will ask you to see the effect that changing either the scale factor [b][color=#ff00ff](k)[/color][/b] or the center of dilation [b][color=#0000ff](point D)[/color][/b] has on the equations of the pre-image.[b] After performing each dilation, please convert each equation into slope-intercept form and then write your answer to the question.[/b]
The equation of the pre-image is -2x+3y = 9; rewrite this in slope-intercept form.
What is the slope and y-intercept of the pre-image?
Please move the center of dilation to the origin, then change the scale factor to a integer value of your choice. Write down the equation of the image and put it into slope intercept form.
What happened to the slope? What happened to the y-intercept?
[b]WITHOUT USING THE GEOGEBRA GRAPH (we will know if you are lying to us. We always know),[/b] what would you expect the equation of the line y = 2x + 3 to be after a dilation centered at the origin with a scale factor of 3?
Please move the center of dilation to a point on the line, then change the scale factor to a integer value of your choice. Write down the equation of the image and put it into slope intercept form.
What happened to the slope? What happened to the y-intercept?
[b]WITHOUT USING THE GEOGEBRA GRAPH (we will know if you are lying to us. We always know),[/b] what would you expect the equation of the line y = 2x + 3 to be after a dilation centered on the line with a scale factor of 3?
Please move the center of dilation anywhere on the coordinate plane that is NOT the origin or a point on the line, then change the scale factor to a integer value of your choice. Write down the equation of the image and put it into slope intercept form.
What happened to the slope? What happened to the y-intercept?
[b]WITHOUT USING THE GEOGEBRA GRAPH (we will know if you are lying to us. We always know),[/b] what would you expect the equation of the line y = 2x + 3 to be after a dilation centered at point (1,3) with a scale factor of 3?