Question

Given y=3x - 4, write an equation that is shifted down 10 and is less steep.

Answer 1

Answer:

y = ½x - 14

Step-by-step explanation:

Given the linear equation, y = 3x - 4, where the slope, m = 3, and the y-intercept is (0, -4):

The slope of a linear equation represents the steepness of the line's graph. The higher the value of the slope, the steeper the line. Hence, the slope of the other line must be less than three, but is greater than zero: 0 < m < 3.   (a negative slope will show a declining line).  

Next, the vertical translation of the line involves changing the value of the parent graph's y-intercept. Since the prompt states that the equation must represent a downward vertical shift of 10 units, then the y-intercept of the other line must be (0, -14).

The linear equation that I have chosen that meets the requirements of the given prompt is: y = ½x - 14.  You're more than welcome to choose a different slope, as long as it is less than 3, but is greater than 0 (must be a positive slope).

Attached is a graph of both equations, to demonstrate that the other equation represents a graph with a steeper slope than the original graph.