Question

Write the point-slope form of the equation for a line that passes through (6, –1) with a slope of 2.

The value of x1 is
.

The value of y1 is
.

The point-slope form of the equation is
.

Answer 1

To write the point-slope form of the equation of a line, we use the formula:

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

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

Given:
- Point \( (x_1, y_1) = (6, -1) \)
- Slope \( m = 2 \)

Now we can identify the values:
- The value of \( x_1 \) is \( 6 \).
- The value of \( y_1 \) is \( -1 \).

Now, substituting these values into the point-slope form of the equation:

\[ y - (-1) = 2(x - 6) \]

This simplifies to:

\[ y + 1 = 2(x - 6) \]

So the point-slope form of the equation is:

\[ y + 1 = 2(x - 6) \]

To summarize:
- The value of \( x_1 \) is **6**.
- The value of \( y_1 \) is **-1**.
- The point-slope form of the equation is **\( y + 1 = 2(x - 6) \)**.