ind the slope of the line $$ y=5 x+12 $$

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UpStudy AI · Accepted Answer

The given equation of the line is:

$$ y = 5x + 12 $$

This equation is in the **slope-intercept form**, which is:

$$ y = mx + b $$

Where:
- $$ m $$ is the **slope** of the line.
- $$ b $$ is the **y-intercept** (the point where the line crosses the y-axis).

Comparing the given equation to the slope-intercept form:

- $$ m = 5 $$
- $$ b = 12 $$

**Therefore, the slope of the line is 5.**

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**Understanding the Slope:**

- The **slope** indicates the steepness of the line.
- A slope of **5** means that for every unit increase in $$ x $$, $$ y $$ increases by 5 units.
- Graphically, the line rises sharply as you move from left to right.

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**Example:**

If $$ x = 0 $$:
$$ y = 5(0) + 12 = 12 $$
So, the point (0, 12) is on the line.

If $$ x = 1 $$:
$$ y = 5(1) + 12 = 17 $$
So, the point (1, 17) is on the line.

The change in $$ y $$ divided by the change in $$ x $$ between these two points is:
$$ \frac{17 - 12}{1 - 0} = \frac{5}{1} = 5 $$

This confirms that the slope is indeed 5.
The slope of the line $$ y = 5x + 12 $$ is 5.

ind the slope of the line

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