Once we have the slope and a point on the line, how is the equation written in point-slope form?

Question

The slope is substituted in for m.

The x-value of the point is substituted in for x
1
​
, and the y-value is substituted in for y
1
​
.

The x-value of the point is substituted in for y
1
​
, and the y-value is substituted in for x
1
​
.

Two of these are correct.

Answer 1

The point-slope form of a linear equation is written as:

\[ y - y_1 = m(x - x_1) \]

where:

• \( m \) is the slope of the line,
• \( (x_1, y_1) \) is a point on the line.

In this form:

1. The slope \( m \) is substituted in for \( m \).
2. The x-coordinate of the point \( x_1 \) is substituted in for \( x_1 \).
3. The y-coordinate of the point \( y_1 \) is substituted in for \( y_1 \).

So, the first two statements are correct:

• The slope is substituted in for \( m \).
• The x-value of the point is substituted in for \( x_1 \), and the y-value is substituted in for \( y_1 \).

Therefore, the answer is: Two of these are correct.