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

Question

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

Answer 1

The equation of a line is:

 

y = mx + b

 

Where m is the slope and b is the y-intercept.  Your equation is y = 2x + 3, so m = 2 and b = 3.  The slope m defines the steepness of the line.  A line three times as steep would have a slope of 3m: in your case 3*2 = 6.  If you slide the whole line down 4 units, the y-intercept becomes 3 - 4 = -1.  So the new equation for the line becomes:

 

y = 6x - 1