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: $(1, - 2)$; $m = - 1$
equation: $y - \square = \square(x - \square)$

Explanation:

Step1: Identify \( y_1 \)

From the point \( (1, -2) \), \( y_1 = -2 \). So in the point - slope form \( y - y_1=m(x - x_1) \), we have \( y-(-2)=m(x - x_1) \), which simplifies to \( y + 2=m(x - x_1) \) (but we need to follow the form \( y - y_1\), so \( y_1=-2 \) means \( y-(-2)=y + 2\), but in the given box form, we need to write \( y - y_1\), so \( y_1=-2 \), so the first box is \( (-2) \) (but since it's \( y - y_1\), and \( y_1=-2 \), \( y-(-2)=y + 2\), but the form is \( y-\square\), so \( \square=- 2\) (because \( y-(-2)=y + 2\) is equivalent to \( y-(-2)\))? Wait, no. Wait the point - slope form is \( y - y_1=m(x - x_1) \). Given the point \( (x_1,y_1)=(1,-2) \), so \( x_1 = 1\), \( y_1=-2 \), and \( m=-1 \).

Step2: Substitute \( y_1\), \( m \) and \( x_1 \)

Substitute \( y_1=-2 \), \( m = - 1\) and \( x_1 = 1\) into the point - slope form \( y - y_1=m(x - x_1) \).

We get \( y-(-2)=-1(x - 1) \), which is \( y + 2=-1(x - 1) \). But the given form is \( y-\square=\square(x-\square) \). So for \( y - y_1\), since \( y_1=-2 \), \( y-(-2)=y + 2\) is the same as \( y-(-2) \), so the first box (the one after \( y-\)) is \( - 2\) (because \( y-(-2)\) is the left - hand side). The middle box (the slope \( m\)) is \( - 1\), and the last box (the \( x_1\)) is \( 1\).

Answer:

The first box: \(-2\), the second box: \(-1\), the third box: \(1\)

So the equation is \( y-(-2)=-1(x - 1) \), filling in the boxes: \( y-\boxed{-2}=\boxed{-1}(x-\boxed{1}) \)