The equation given is $y = -x + 8$, and it's in slope-intercept form, $y = mx + b$, where $m$ is the slope, and $b$ is the y-intercept.

Key Points to Graph This Line:

1. Y-Intercept ($b$):

   • The y-intercept is $b = 8$. This means the line crosses the y-axis at the point $(0, 8)$.

2. Slope ($m$):

   • The slope is $m = -1$. Slope is defined as $\frac{\text{rise}}{\text{run}}$. Here, $-1$ means that for every 1 unit you move to the right (positive x-direction), the line moves 1 unit down (negative y-direction).

Steps to Plot:

1. Start at the y-intercept, $(0, 8)$, and place a point there.
2. Use the slope $-1$:
   • From $(0, 8)$, move 1 unit to the right and 1 unit down. This lands you at the point $(1, 7)$.
3. Plot another point at $(1, 7)$.
4. Draw the straight line through these two points.

Verify Additional Points:

You can verify the equation with other points:

• If $x = 2$, then $y = -2 + 8 = 6$, so $(2, 6)$ lies on the line.

Would you like a more detailed explanation or visual assistance? Let me know!

Related Questions:

1. What does the slope-intercept form of a line represent geometrically?
2. How do you find the slope of a line given two points?
3. What happens to the graph if the slope is positive instead of negative?
4. How do vertical or horizontal lines differ from diagonal ones?
5. Can this line ever intersect the x-axis? If yes, where?

Tip:

Always start plotting with the y-intercept, as it simplifies graphing significantly!