4) graph all 3 lines on the same grid. state the slope, rise, run and y - intercept. label the lines.
①: ( y = x + 2 )
slope: ( m = )
rise =
run =
y - intercept: ( b = )
②: ( y = x - 4 )
slope: ( m = )
rise =
run =
y - intercept: ( b = )
③: ( y = x )
slope: ( m = )
rise =
run =
y - intercept: ( b = )
(there is a coordinate grid and a pencil in the image, and some hand - written answers on the original paper)

Question

Accepted Answer

To solve the problem of graphing the three lines $ y = x + 2 $, $ y = x - 4 $, and $ y = x $, we analyze each line using the slope - intercept form $ y=mx + b $, where $ m $ is the slope and $ b $ is the y - intercept. The slope $ m=\frac{\text{rise}}{\text{run}} $.

### For Line 1: $ y=x + 2 $
- **Step 1: Identify the slope ($ m $) and y - intercept ($ b $)**
    - In the slope - intercept form $ y=mx + b $, for the equation $ y=x + 2 $, we can rewrite it as $ y = 1x+2 $. So, the slope $ m = 1$ and the y - intercept $ b = 2 $.
    - Since the slope $ m=\frac{\text{rise}}{\text{run}}=1=\frac{1}{1} $, the rise (change in $ y $) is $ 1 $ and the run (change in $ x $) is $ 1 $.
- **Step 2: Graph the line**
    - Start by plotting the y - intercept. The y - intercept is $ 2 $, so we plot the point $ (0,2) $ on the y - axis.
    - Then, use the slope to find the next point. Since the rise is $ 1 $ and the run is $ 1 $, from the point $ (0,2) $, we move up $ 1 $ unit and then to the right $ 1 $ unit to get the point $ (1,3) $. We can continue this process to plot more points and then draw a straight line through the plotted points.

### For Line 2: $ y=x - 4 $
- **Step 1: Identify the slope ($ m $) and y - intercept ($ b $)**
    - In the slope - intercept form $ y=mx + b $, for the equation $ y=x - 4 $, we can rewrite it as $ y = 1x-4 $. So, the slope $ m = 1$ and the y - intercept $ b=- 4 $.
    - Since the slope $ m=\frac{\text{rise}}{\text{run}} = 1=\frac{1}{1}$, the rise is $ 1 $ and the run is $ 1 $.
- **Step 2: Graph the line**
    - Start by plotting the y - intercept. The y - intercept is $ - 4 $, so we plot the point $ (0,-4) $ on the y - axis.
    - Then, use the slope to find the next point. Since the rise is $ 1 $ and the run is $ 1 $, from the point $ (0,-4) $, we move up $ 1 $ unit and then to the right $ 1 $ unit to get the point $ (1,-3) $. We can continue this process to plot more points and then draw a straight line through the plotted points.

### For Line 3: $ y=x $
- **Step 1: Identify the slope ($ m $) and y - intercept ($ b $)**
    - In the slope - intercept form $ y=mx + b $, for the equation $ y=x $, we can rewrite it as $ y = 1x+0 $. So, the slope $ m = 1$ and the y - intercept $ b = 0 $.
    - Since the slope $ m=\frac{\text{rise}}{\text{run}}=1=\frac{1}{1}$, the rise is $ 1 $ and the run is $ 1 $.
- **Step 2: Graph the line**
    - Start by plotting the y - intercept. The y - intercept is $ 0 $, so we plot the point $ (0,0) $ (the origin).
    - Then, use the slope to find the next point. Since the rise is $ 1 $ and the run is $ 1 $, from the point $ (0,0) $, we move up $ 1 $ unit and then to the right $ 1 $ unit to get the point $ (1,1) $. We can continue this process to plot more points and then draw a straight line through the plotted points.

### Summary of the properties of the lines:
| Line | Equation | Slope ($ m $) | Rise | Run | Y - intercept ($ b $) |
|------|----------|----------------|------|-----|-------------------------|
| 1 | $ y=x + 2 $ | $ 1 $ | $ 1 $ | $ 1 $ | $ 2 $ |
| 2 | $ y=x - 4 $ | $ 1 $ | $ 1 $ | $ 1 $ | $ - 4 $ |
| 3 | $ y=x $ | $ 1 $ | $ 1 $ | $ 1 $ | $ 0 $ |

When graphing, all three lines are parallel (since they have the same slope $ m = 1$) and are shifted vertically based on their y - intercepts.

Line	Equation	Slope (\( m \))	Rise	Run	Y - intercept (\( b \))
2	\( y=x - 4 \)	\( 1 \)	\( 1 \)	\( 1 \)	\( - 4 \)
3	\( y=x \)	\( 1 \)	\( 1 \)	\( 1 \)	\( 0 \)

Line	Equation	Slope (\( m \))	Rise	Run	Y - intercept (\( b \))
2	\( y=x - 4 \)	\( 1 \)	\( 1 \)	\( 1 \)	\( - 4 \)
3	\( y=x \)	\( 1 \)	\( 1 \)	\( 1 \)	\( 0 \)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

For Line 1: \( y=x + 2 \)

For Line 2: \( y=x - 4 \)

For Line 3: \( y=x \)

Summary of the properties of the lines:

Answer:

For Line 1: \( y=x + 2 \)

For Line 2: \( y=x - 4 \)

For Line 3: \( y=x \)

Summary of the properties of the lines: