Question

What is the point-slope form of the equation of the line that has a slope of 2 and passes through the point ( -5, 4) ?

y- __= 2(x- __ )

Answer 1

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

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

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

In your case, the slope \( m = 2 \) and the point is \( (-5, 4) \). So, \( x_1 = -5 \) and \( y_1 = 4 \).

Substituting these values into the point-slope form, we have:

\[
y - 4 = 2(x - (-5))
\]

This simplifies to:

\[
y - 4 = 2(x + 5)
\]

So, the equation in point-slope form is:

\[
y - 4 = 2(x + 5)
\]

Thus, filling in the blanks in your original expression:

\[
y - 4 = 2(x - (-5))
\]

The final form is:

\[
y - 4 = 2(x + 5)
\]

So, the answer is:

**y - 4 = 2(x + 5)**

where the filled-in blanks would be:

- First blank: 4
- Second blank: -5