- Lines Finding the slope and $$ y $$-Intercept of a line given it Find the $$ y $$-Intercept and the slope of the line. $$ y=-\frac{3}{4} $$ $$ y $$-Intercept: $$ \square $$ slope: $$ \square $$ Explanation Check

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UpStudy AI · Accepted Answer

Sure, let's find the **$$ y $$-Intercept** and the **slope** of the given line:

$$
y = -\frac{3}{4}
$$

### $$ y $$-Intercept:
The $$ y $$-intercept is the point where the line crosses the $$ y $$-axis. This occurs when $$ x = 0 $$.

From the equation $$ y = -\frac{3}{4} $$, it's clear that no matter what value $$ x $$ takes, $$ y $$ is always $$-\frac{3}{4}$$. Therefore, the $$ y $$-intercept is:

$$
\boxed{-\frac{3}{4}}
$$

### Slope:
The slope of a line indicates its steepness and direction. It is usually represented by the coefficient of $$ x $$ in the equation $$ y = mx + b $$, where $$ m $$ is the slope and $$ b $$ is the $$ y $$-intercept.

In the given equation $$ y = -\frac{3}{4} $$, there is no $$ x $$ term present. This implies that the coefficient of $$ x $$ is 0. Therefore, the slope $$ m $$ is:

$$
\boxed{0}
$$

### Explanation:
The equation $$ y = -\frac{3}{4} $$ represents a **horizontal line** because the value of $$ y $$ remains constant regardless of the value of $$ x $$.

- **$$ y $$-Intercept:** Since the line crosses the $$ y $$-axis at $$ y = -\frac{3}{4} $$, the $$ y $$-intercept is $$-\frac{3}{4}$$.
  
- **Slope:** A horizontal line does not rise or fall as $$ x $$ increases; hence, its slope is 0.

### Check:
To verify, consider two points on the line:

1. When $$ x = 0 $$, $$ y = -\frac{3}{4} $$ → Point $$ (0, -\frac{3}{4}) $$
2. When $$ x = 2 $$, $$ y = -\frac{3}{4} $$ → Point $$ (2, -\frac{3}{4}) $$

Calculating the slope between these two points:

$$
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-\frac{3}{4} - (-\frac{3}{4})}{2 - 0} = \frac{0}{2} = 0
$$

This confirms that the slope is indeed 0.
$$ y $$-Intercept: $$-\frac{3}{4}$$ Slope: $$0$$

Lines
Finding the slope and -Intercept of a line given it

Find the -Intercept and the slope of the line.

-Intercept:
slope:
Explanation
Check

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Lines Finding the slope and -Intercept of a line given it Find the -Intercept and the slope of the line. -Intercept: slope: Explanation Check