Let's break this down and find the x- and y-intercepts of the two given equations step-by-step.

Equation 1: $-2x + 8y = 16$

1. Finding the x-intercept:

To find the x-intercept, set $y = 0$ and solve for $x$.

$-2x + 8(0) = 16 \quad \Rightarrow \quad -2x = 16 \quad \Rightarrow \quad x = -8$

So, the x-intercept is $(-8, 0)$.

2. Finding the y-intercept:

To find the y-intercept, set $x = 0$ and solve for $y$.

$-2(0) + 8y = 16 \quad \Rightarrow \quad 8y = 16 \quad \Rightarrow \quad y = 2$

So, the y-intercept is $(0, 2)$.

Equation 2: $x - 2y = 6$

1. Finding the x-intercept:

Set $y = 0$ and solve for $x$.

$x - 2(0) = 6 \quad \Rightarrow \quad x = 6$

So, the x-intercept is $(6, 0)$.

2. Finding the y-intercept:

Set $x = 0$ and solve for $y$.

$0 - 2y = 6 \quad \Rightarrow \quad -2y = 6 \quad \Rightarrow \quad y = -3$

So, the y-intercept is $(0, -3)$.

Graphing the Lines:

1. For the first equation, plot the points $(-8, 0)$ and $(0, 2)$, then draw a straight line through them.
2. For the second equation, plot the points $(6, 0)$ and $(0, -3)$, then draw a straight line through them.

Would you like me to generate a graph of these lines for you?

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Related Questions:

1. How can we use intercepts to graph any linear equation?
2. What is the general method to find intercepts for any linear equation?
3. How can you determine the slope of a line from the intercepts?
4. How do the intercepts of a line relate to its equation in slope-intercept form?
5. What happens to the intercepts if we modify the coefficients in the equation?

Tip:

To quickly graph a line from an equation, always start by finding the intercepts. They give you two easy points to plot, and from there, you can sketch the line with confidence!