To complete the table and graph the equation [tex]\(2x - 5y = 10\)[/tex], we first need to find the value of [tex]\(y\)[/tex] when [tex]\(x = 0\)[/tex].
1. Substitute [tex]\(x = 0\)[/tex] into the equation [tex]\(2x - 5y = 10\)[/tex]:
[tex]\[
2(0) - 5y = 10
\][/tex]
Simplifies to:
[tex]\[
-5y = 10
\][/tex]
To solve for [tex]\(y\)[/tex], divide both sides by [tex]\(-5\)[/tex]:
[tex]\[
y = \frac{10}{-5}
\][/tex]
Simplifying this fraction, we get:
[tex]\[
y = -2
\][/tex]
So, when [tex]\(x = 0\)[/tex], [tex]\(y = -2\)[/tex].
Therefore, the completed table is:
\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
0 & -2 \\
\hline
\end{tabular}
To graph the equation [tex]\(2x - 5y = 10\)[/tex], follow these steps:
1. Find two points on the line: One point is already identified from the table, which is [tex]\((0, -2)\)[/tex]. We can find another point by choosing another value for [tex]\(x\)[/tex] and solving for [tex]\(y\)[/tex].
Let's find [tex]\(y\)[/tex] when [tex]\(x = 5\)[/tex]:
[tex]\[
2(5) - 5y = 10
\][/tex]
Simplifies to:
[tex]\[
10 - 5y = 10
\][/tex]
Subtract 10 from both sides:
[tex]\[
-5y = 0
\][/tex]
Divide by [tex]\(-5\)[/tex]:
[tex]\[
y = 0
\][/tex]
So, another point is [tex]\((5, 0)\)[/tex].
2. Plot these points on the coordinate plane:
- Plot the point [tex]\((0, -2)\)[/tex].
- Plot the point [tex]\((5, 0)\)[/tex].
3. Draw the line: Connect these two points with a straight line, extending it in both directions.
By doing this, you'll have the graph of the equation [tex]\(2x - 5y = 10\)[/tex]. The line will cross the vertical axis (y-axis) at [tex]\((0, -2)\)[/tex] and the horizontal axis (x-axis) at [tex]\((5, 0)\)[/tex]. This line represents all the solutions to the equation [tex]\(2x - 5y = 10\)[/tex].
