Sure, let's tackle the problem step by step.
### Part (a): Complete the table of values for [tex]\( y = 6 - 2x \)[/tex]
For [tex]\( x = 0, 1, 2, 3, 4, 5 \)[/tex], we can substitute each value of [tex]\( x \)[/tex] into the equation [tex]\( y = 6 - 2x \)[/tex] to find the corresponding [tex]\( y \)[/tex] values.
1. When [tex]\( x = 0 \)[/tex]:
[tex]\[
y = 6 - 2(0) = 6 - 0 = 6
\][/tex]
2. When [tex]\( x = 1 \)[/tex]:
[tex]\[
y = 6 - 2(1) = 6 - 2 = 4
\][/tex]
3. When [tex]\( x = 2 \)[/tex]:
[tex]\[
y = 6 - 2(2) = 6 - 4 = 2
\][/tex]
4. When [tex]\( x = 3 \)[/tex]:
[tex]\[
y = 6 - 2(3) = 6 - 6 = 0
\][/tex]
5. When [tex]\( x = 4 \)[/tex]:
[tex]\[
y = 6 - 2(4) = 6 - 8 = -2
\][/tex]
6. When [tex]\( x = 5 \)[/tex]:
[tex]\[
y = 6 - 2(5) = 6 - 10 = -4
\][/tex]
So, the completed table of values should be:
[tex]\[
\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
$x$ & 0 & 1 & 2 & 3 & 4 & 5 \\
\hline
$y$ & 6 & 4 & 2 & 0 & -2 & -4 \\
\hline
\end{tabular}
\][/tex]
### Part (b): Draw the graph of [tex]\( y = 6 - 2x \)[/tex]
To draw the graph, you can plot the points from the table of values on the grid and then connect them with a straight line. The points to plot are:
- (0, 6)
- (1, 4)
- (2, 2)
- (3, 0)
- (4, -2)
- (5, -4)
These points lie on a straight line because the equation [tex]\( y = 6 - 2x \)[/tex] represents a linear function.
### Part (c): Solve [tex]\( 6 - 2x = 3 \)[/tex]
To solve for [tex]\( x \)[/tex]:
1. Start with the equation:
[tex]\[
6 - 2x = 3
\][/tex]
2. Subtract 6 from both sides to isolate the term involving [tex]\( x \)[/tex]:
[tex]\[
-2x = 3 - 6
\][/tex]
3. Simplify the right-hand side:
[tex]\[
-2x = -3
\][/tex]
4. Divide both sides by -2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{-3}{-2} = 1.5
\][/tex]
So, the solution to the equation [tex]\( 6 - 2x = 3 \)[/tex] is:
[tex]\[
x = 1.5
\][/tex]
