line equation

Question

imagine a line with the equation y=2x+3. the line is made 3 times as steep and then the whole line slides down four units. what is the new equation now. 

Explain 

Answer 1

When we are talking about steepness of a line, we are focusing on the slope of the line.  In this equation, the slope is 2.  We want this slope to be 3 times as steep when the whole line slides down 4 units.

 

To make this steeper, we increase the rise of the slope.  In this case, the rise is 2 and the run is 1.  Multiply the value of the rise by three to make it three times as steep.  Our new rise is 6, making the slope 6.

 

Since the y-intercept is 3, we have to move down 4 units from that point.  The new y-intercept is -1.

 

 

Therefore, the new equation is

 

y = 6x - 1