Question

What is the slope of the line?
\[y-3=5(x-2)\]
Choose 1 answer:
Choose 1 answer:
(Choice A)

\[-\dfrac{4}5\]
A

\[-\dfrac{4}5\]
(Choice B)

\[\dfrac{1}5\]
B

\[\dfrac{1}5\]
(Choice C)
\[5\]
C
\[5\]
(Choice D)
\[1\]
D
\[1\]

Answer 1

To find the slope of the line given by the equation

\[
y - 3 = 5(x - 2),
\]

we can compare this to the slope-intercept form of a linear equation, which is written as

\[
y = mx + b,
\]

where \( m \) is the slope.

The equation can be rewritten in slope-intercept form:

1. Distribute the \( 5 \) on the right side:
\[
y - 3 = 5x - 10.
\]

2. Add \( 3 \) to both sides:
\[
y = 5x - 10 + 3,
\]
which simplifies to
\[
y = 5x - 7.
\]

Now, we can clearly see that the slope \( m \) is \( 5 \).

Thus, the slope of the line is

\[
\boxed{5}.
\]

The correct answer is **(Choice C) 5**.