throwback:
find the slope of the line from the graph:
$m = \frac{rise}{run} = $
$m = \frac{rise}{run} = $
$m = \frac{rise}{run} = $
$m = \frac{rise}{run} = $
find the slope of the line through the two points (use the slope formula)
(8,10) and (5,3)
(-2,4) and (-2,7)
(5,1) and (-4,1)
(-3,1) and (3,-1)
5.5 key feature of linear graphs
identify the following key features from the graph:
x-intercept:
y-intercept:
slope:
use the following key features to graph the line:
x-intercept: (3,0)
y-intercept: (0,6)
slope: $m = -2$
5.6 slope-intercept form
given the following equations in slope intercept form, identify the slope and y-intercept:
slope:
y = 3x + 5
y-intercept:
slope:
y = -\frac{1}{5}x - 1
y-intercept:

Question

Accepted Answer

### Part 1: Find the slope of the line through the two points (use the slope formula)

#### 1. For points $(8, 10)$ and $(5, 3)$
# Explanation:
## Step 1: Recall the slope formula
The slope formula is $ m = \frac{y_2 - y_1}{x_2 - x_1} $, where $(x_1, y_1) = (8, 10)$ and $(x_2, y_2) = (5, 3)$.
## Step 2: Substitute the values into the formula
$ m = \frac{3 - 10}{5 - 8} = \frac{-7}{-3} = \frac{7}{3} $
# Answer:
The slope is $\frac{7}{3}$

#### 2. For points $(-2, 4)$ and $(-2, 7)$
# Explanation:
## Step 1: Recall the slope formula
The slope formula is $ m = \frac{y_2 - y_1}{x_2 - x_1} $, where $(x_1, y_1) = (-2, 4)$ and $(x_2, y_2) = (-2, 7)$.
## Step 2: Substitute the values into the formula
$ m = \frac{7 - 4}{-2 - (-2)} = \frac{3}{0} $, which is undefined (vertical line).
# Answer:
The slope is undefined

#### 3. For points $(5, 1)$ and $(-4, 1)$
# Explanation:
## Step 1: Recall the slope formula
The slope formula is $ m = \frac{y_2 - y_1}{x_2 - x_1} $, where $(x_1, y_1) = (5, 1)$ and $(x_2, y_2) = (-4, 1)$.
## Step 2: Substitute the values into the formula
$ m = \frac{1 - 1}{-4 - 5} = \frac{0}{-9} = 0 $ (horizontal line)
# Answer:
The slope is $0$

#### 4. For points $(-3, 1)$ and $(3, -1)$
# Explanation:
## Step 1: Recall the slope formula
The slope formula is $ m = \frac{y_2 - y_1}{x_2 - x_1} $, where $(x_1, y_1) = (-3, 1)$ and $(x_2, y_2) = (3, -1)$.
## Step 2: Substitute the values into the formula
$ m = \frac{-1 - 1}{3 - (-3)} = \frac{-2}{6} = -\frac{1}{3} $
# Answer:
The slope is $-\frac{1}{3}$

### Part 2: Identify the key features from the graph (x-intercept, y-intercept, slope)
For the given graph:
- **x-intercept**: The x-intercept is the point where the line crosses the x-axis. From the graph, the line crosses the x-axis at $(2, 0)$, so the x-intercept is $2$ (or the point $(2, 0)$).
- **y-intercept**: The y-intercept is the point where the line crosses the y-axis. From the graph, the line crosses the y-axis at $(0, 3)$, so the y-intercept is $3$ (or the point $(0, 3)$).
- **slope**: To find the slope, we use two points on the line, say $(0, 3)$ and $(2, 0)$. Using the slope formula $ m = \frac{y_2 - y_1}{x_2 - x_1} $, we get $ m = \frac{0 - 3}{2 - 0} = \frac{-3}{2} = -\frac{3}{2} $.
# Brief Explanations:
- x-intercept: The line crosses the x - axis at $x = 2$ (point $(2,0)$).
- y-intercept: The line crosses the y - axis at $y = 3$ (point $(0,3)$).
- slope: Using points $(0,3)$ and $(2,0)$ in the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we calculate $m =-\frac{3}{2}$.
# Answer:
x-intercept: $2$ (or $(2, 0)$)
y-intercept: $3$ (or $(0, 3)$)
slope: $-\frac{3}{2}$

### Part 3: Given the equations in slope - intercept form, identify the slope and y - intercept
The slope - intercept form of a line is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept.

#### 1. For the equation $y = 3x+5$
- **Slope**: Comparing with $y = mx + b$, we see that $m = 3$.
- **y - intercept**: Comparing with $y = mx + b$, we see that $b = 5$.

#### 2. For the equation $y=-\frac{1}{5}x - 1$
- **Slope**: Comparing with $y = mx + b$, we see that $m=-\frac{1}{5}$.
- **y - intercept**: Comparing with $y = mx + b$, we see that $b=-1$.
# Brief Explanations:
- For $y = 3x + 5$, in the slope - intercept form $y=mx + b$, $m = 3$ (slope) and $b = 5$ (y - intercept).
- For $y=-\frac{1}{5}x-1$, in the slope - intercept form $y = mx + b$, $m=-\frac{1}{5}$ (slope) and $b=-1$ (y - intercept).
# Answer:
For $y = 3x+5$:
Slope: $3$
y - intercept: $5$

For $y=-\frac{1}{5}x - 1$:
Slope: $-\frac{1}{5}$
y - intercept: $-1$

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QUESTION IMAGE

Question

Explanation:

Part 1: Find the slope of the line through the two points (use the slope formula)

1. For points \((8, 10)\) and \((5, 3)\)

Step 1: Recall the slope formula

Step 2: Substitute the values into the formula

Step 1: Recall the slope formula

Step 2: Substitute the values into the formula

Step 1: Recall the slope formula

Step 2: Substitute the values into the formula

Answer:

2. For points \((-2, 4)\) and \((-2, 7)\)