https://file.aiquickdraw.com/mathbot/file/17266637499276bs1niox.jpg

Let's solve both of the questions from the image:

### 1. **Given the equation \( y = 5x - 2 \):**
- The equation is in the slope-intercept form \( y = mx + b \), where \( m = 5 \) (the slope) and \( b = -2 \) (the y-intercept).

**The y-intercept is:**  
The y-intercept occurs when \( x = 0 \). Substituting \( x = 0 \) into the equation:
\[
y = 5(0) - 2 = -2
\]
Thus, the y-intercept is \( (0, -2) \).

**The x-intercept is:**  
The x-intercept occurs when \( y = 0 \). Set \( y = 0 \) and solve for \( x \):
\[
0 = 5x - 2
\]
\[
5x = 2 \quad \Rightarrow \quad x = \frac{2}{5}
\]
Thus, the x-intercept is \( \left( \frac{2}{5}, 0 \right) \).

---

### 2. **Factor Completely: \( 8x^3 - 27y^3 \):**

This is a difference of cubes. The formula for factoring a difference of cubes is:
\[
a^3 - b^3 = (a - b)(a^2 + ab + b^2)
\]

Here, \( 8x^3 = (2x)^3 \) and \( 27y^3 = (3y)^3 \), so:
\[
8x^3 - 27y^3 = (2x - 3y)((2x)^2 + (2x)(3y) + (3y)^2)
\]

Now, simplifying the second factor:
\[
(2x - 3y)(4x^2 + 6xy + 9y^2)
\]

Thus, the complete factorization is:
\[
8x^3 - 27y^3 = (2x - 3y)(4x^2 + 6xy + 9y^2)
\]

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Would you like more details or have any other questions?

Here are 5 related questions you might want to explore:
1. How do you find the intercepts of any linear equation?
2. What is the general form of the equation of a line?
3. How do you recognize a sum of cubes and factor it?
4. What is the geometric interpretation of intercepts in a graph?
5. Can the difference of cubes formula be extended to higher powers?

**Tip:** When factoring cubes, always check if the expression fits either a sum of cubes or a difference of cubes for easier factoring.

Factor Completely: 8x^3 - 27y^3 and intercepts of y = 5x - 2

Solve the linear equation y = 5x - 2 to find its x and y intercepts, and learn how to completely factor 8x^3 - 27y^3 using the difference of cubes formula. This step-by-step guide covers key algebraic concepts for students in Grades 9-10.

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