Question

use the given information to write the equation of the line in point - slope form. point slope form: $y - y_1 = m(x - x_1)$
p: $(5, - 1)$; $m = 2$
equation: $y - \square = \square(x - \square)$

Explanation:

Step1: Identify \( y_1 \) from the point

The point is \( (5, -1) \), so \( y_1 = -1 \).

Step2: Identify \( m \) (slope)

Given \( m = 2 \).

Step3: Identify \( x_1 \) from the point

The point is \( (5, -1) \), so \( x_1 = 5 \).

Step4: Substitute into point - slope form

The point - slope form is \( y - y_1=m(x - x_1) \). Substituting \( y_1=-1 \), \( m = 2 \) and \( x_1 = 5 \), we get \( y-(-1)=2(x - 5) \), which simplifies to \( y + 1=2(x - 5) \). But for the given blanks, we use the values of \( y_1=-1 \), \( m = 2 \) and \( x_1 = 5 \) directly in the form \( y - y_1=m(x - x_1) \).

Answer:

\( y-\boldsymbol{(-1)}=\boldsymbol{2}(x-\boldsymbol{5}) \) (or filling the blanks as \( y - (-1)=2(x - 5) \) which is equivalent to \( y+1 = 2(x - 5) \), but in the form of the blanks \( y-\underline{-1}=\underline{2}(x-\underline{5}) \))