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Accepted Answer

### Part 1: Match the following (Lines and Slopes)
#### 1.
# Explanation:
Perpendicular lines have slopes that are negative reciprocals (their product is -1). So we match with "Perpendicular".
## Step1: Recall slope property of perpendicular lines.
Perpendicular lines: slopes are negative reciprocals.
# Answer:
1. b. Perpendicular

#### 2.
# Explanation:
We know that $\tan(\theta)=\text{slope}$. If slope = 1, then $\tan(\theta) = 1$, and $\theta = 45^\circ$ (since $\tan(45^\circ)=1$).
## Step1: Use $\tan(\theta)=\text{slope}$ formula.
Given slope = 1, solve $\tan(\theta)=1$.
## Step2: Find $\theta$ where $\tan(\theta)=1$.
$\theta = 45^\circ$ (as $\tan(45^\circ)=1$).
# Answer:
2. c. $45^\circ$

#### 3.
# Explanation:
The definition of the slope of a line is the ratio of the rise (vertical change) to the run (horizontal change).
## Step1: Recall the definition of slope.
Slope $=\frac{\text{rise}}{\text{run}}$.
# Answer:
3. f. Slope

#### 4.
# Explanation:
A vertical line has an undefined slope (since the run is 0, and division by 0 is undefined, so the slope is considered infinity or undefined).
## Step1: Recall slope of vertical line.
Vertical line: run $= 0$, so slope $=\frac{\text{rise}}{0}$ (undefined).
# Answer:
4. d. Vertical

#### 5. (Note: There might be a typo, but assuming it's "parallel" as lines with the same slope are parallel)
# Explanation:
Lines with the same slope are parallel (they never intersect and have the same direction).
## Step1: Recall the property of parallel lines.
Parallel lines: same slope.
# Answer:
5. g. Parallel

#### 6. (Assuming it's a repeat or typo, but same as 5, lines with same slope are parallel)
# Explanation:
Lines with the same slope are parallel (they never intersect and have the same direction).
## Step1: Recall the property of parallel lines.
Parallel lines: same slope.
# Answer:
6. g. Parallel

### Part 2: Match the following (Forms of Linear Functions)
#### 1.
# Explanation:
The standard form of a linear function is generally written as $ax + by = c$ (or sometimes $ax + by + c = 0$, but the more common standard form is $ax + by = c$). Wait, let's check:

- Option c: $ax + by = c$ is a standard form. Option a: $ax + by + c = 0$ is also a general linear equation form. But typically, standard form is $ax + by = c$ (where $a,b,c$ are integers, $a\geq0$). However, sometimes both are considered, but let's check the options.

Wait, let's re - check:

The standard form of a linear function: The standard form is usually $Ax + By = C$ (where $A$, $B$, and $C$ are integers, and $A\geq0$). So option c: $ax + by = c$ matches.

## Step1: Recall standard form of linear function.
Standard form: $Ax + By = C$ (or $ax + by = c$ in the options).
# Answer:
1. c. $ax + by = c$

#### 2.
# Explanation:
The slope - intercept form of a linear function is $y=mx + b$, where $m$ is the slope and $b$ is the y - intercept.
## Step1: Recall slope - intercept form.
Slope - intercept form: $y = mx + b$.
# Answer:
2. d. $y=mx + b$

#### 3.
# Explanation:
The formula to find the slope of a line between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.
## Step1: Recall the slope formula between two points.
Slope $m=\frac{y_2 - y_1}{x_2 - x_1}$ for points $(x_1,y_1)$ and $(x_2,y_2)$.
# Answer:
3. b. $m=\frac{y_2 - y_1}{x_2 - x_1}$

#### 4.
# Explanation:
The point - slope form of a linear function is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope.
## Step1: Recall the point - slope form.
Point - slope form: $y - y_1=m(x - x_1)$ (using point $(x_1,y_1)$ and slope $m$).
# Answer:
4. e. $y - y_1=m(x - x_1)$

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QUESTION IMAGE

Question

Explanation:

Part 1: Match the following (Lines and Slopes)

1.

Step1: Recall slope property of perpendicular lines.

Step1: Use \(\tan(\theta)=\text{slope}\) formula.

Step2: Find \(\theta\) where \(\tan(\theta)=1\).

Step1: Recall the definition of slope.

Answer:

2.