Question

Describe the vertical translation between y=17x
and y=2x−23
.

Option #1: 23 points above the graph y=17x


Option #2: 23 points below the graph y=17x


(1 point)
Option #

Answer 1

To determine the vertical translation between the functions \( y = 17x \) and \( y = 2x - 23 \), we can analyze the two equations.

1. The line \( y = 17x \) has a slope of 17 and no vertical shift (y-intercept is 0).
2. The line \( y = 2x - 23 \) has a slope of 2 and a vertical shift (y-intercept is -23).

To find the translation vertically, we can compare the y-values at a specific x-coordinate.

For example, let's calculate the y-value of each graph when \( x = 0 \):

- For \( y = 17x \):
\[
y = 17(0) = 0
\]

- For \( y = 2x - 23 \):
\[
y = 2(0) - 23 = -23
\]

The difference in y-values is:
\[
0 - (-23) = 23
\]

This means that the graph of \( y = 2x - 23 \) is 23 points below the graph of \( y = 17x \) when comparing their y-intercepts.

Therefore, the correct option is:

**Option #2: 23 points below the graph \( y = 17x \)**.