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: $8x^3 - 27y^3 = (2x - 3y)(4x^2 + 6xy + 9y^2)$

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.