To analyze the function [tex]\( -x + y = -2 \)[/tex] and determine the true statements about it, we will follow these steps:
### Step 1: Rewrite the equation in slope-intercept form
First, we will manipulate the given equation to isolate [tex]\( y \)[/tex]:
[tex]\[ -x + y = -2 \][/tex]
Adding [tex]\( x \)[/tex] to both sides, we get:
[tex]\[ y = x - 2 \][/tex]
This is the slope-intercept form, [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
### Step 2: Identify the slope and y-intercept
From the equation [tex]\( y = x - 2 \)[/tex]:
- The slope [tex]\( m \)[/tex] is [tex]\( 1 \)[/tex].
- The y-intercept [tex]\( b \)[/tex] is [tex]\( -2 \)[/tex].
### Step 3: Determine the x-intercept
To find the x-intercept, set [tex]\( y \)[/tex] to [tex]\( 0 \)[/tex] and solve for [tex]\( x \)[/tex]:
[tex]\[ 0 = x - 2 \][/tex]
Adding [tex]\( 2 \)[/tex] to both sides, we get:
[tex]\[ x = 2 \][/tex]
So, the x-intercept is [tex]\( 2 \)[/tex].
### Step 4: Determine the direction of the line
Since the slope [tex]\( m \)[/tex] is [tex]\( 1 \)[/tex], which is positive, the line rises from left to right.
### Summary of true statements:
1. Slope of the function: The slope is [tex]\( 1 \)[/tex].
2. Y-intercept of the function: The y-intercept is [tex]\( -2 \)[/tex].
3. X-intercept of the function: The x-intercept is [tex]\( 2 \)[/tex].
4. The line rises from left to right because the slope is positive.
All these statements have been verified to be true based on the given function.
