A line with the equation y=7x−3

Question

𝑦
=
7
𝑥
−
3
is drawn on the coordinate plane. The line is then translated 5 units to the left and 2 units up. Which statement is true?(1 point)
Responses

The slope of the translated line remains 7.
The slope of the translated line remains 7.

The slope of the translated line becomes 7+5, or 12.
The slope of the translated line becomes 7+5, or 12.

The slope of the translated line becomes 7+2, or 9.
The slope of the translated line becomes 7+2, or 9.

The slope of the translated line becomes 7–5, or 2.

Answer 1

When a line is translated, its slope remains unchanged. Only the position of the line on the coordinate plane changes.

In this case, the original line has the equation \( y = 7x - 3 \), which has a slope of 7. After translating the line 5 units to the left and 2 units up, the new line will also have a slope of 7.

So the correct statement is:

The slope of the translated line remains 7.