Sure, let's solve the system by graphing the equation [tex]\( Sy = -x + 8 \)[/tex]. Note that I assume "Sy" is just "y" based on a typical linear equation format. If that is incorrect, please provide additional context.
Here are the steps to graph the equation:
1. Rewrite the equation: Ensure it's in the form [tex]\( y = mx + b \)[/tex]. In this case, the equation is already in the slope-intercept form:
[tex]\[
y = -x + 8
\][/tex]
2. Identify the slope and y-intercept:
- The slope (m) is the coefficient of [tex]\( x \)[/tex], which is [tex]\( -1 \)[/tex].
- The y-intercept (b) is [tex]\( 8 \)[/tex]. This means the line crosses the y-axis at [tex]\( (0, 8) \)[/tex].
3. Plot the y-intercept on the graph: Start at point [tex]\( (0, 8) \)[/tex] on the y-axis.
4. Use the slope to find another point:
- The slope [tex]\( -1 \)[/tex] can be interpreted as a ratio [tex]\( \frac{-1}{1} \)[/tex], meaning for every 1 unit you move to the right (positive direction on the x-axis), you move 1 unit down (negative direction on the y-axis).
- From the y-intercept [tex]\( (0, 8) \)[/tex], move 1 unit to the right to [tex]\( (1, 8) \)[/tex] and then 1 unit down to [tex]\( (1, 7) \)[/tex]. This gives you the second point [tex]\( (1, 7) \)[/tex].
5. Draw the line: Connect the points [tex]\( (0, 8) \)[/tex] and [tex]\( (1, 7) \)[/tex] with a straight line. Continue the line in both directions to fully cover the graph.
6. Check additional points (optional): For accuracy, you can check additional points. For instance, when [tex]\( x = -2 \)[/tex]:
[tex]\[
y = -(-2) + 8 = 2 + 8 = 10
\][/tex]
So, [tex]\( (-2, 10) \)[/tex] should also lie on the line.
When graphing, ensure the line is straight and extends infinitely in both directions, marked with arrows.
The graph of the equation [tex]\( y = -x + 8 \)[/tex] will show the relationship between [tex]\( y \)[/tex] and [tex]\( x \)[/tex], allowing you to see the solution set of the equation visually.
