To plot the [tex]\(x\)[/tex]- and [tex]\(y\)[/tex]-intercepts and use them to graph the equation [tex]\(5x - 3y = 15\)[/tex], follow these steps:
1. Find the [tex]\(x\)[/tex]-intercept:
The [tex]\(x\)[/tex]-intercept is the point where the line crosses the [tex]\(x\)[/tex]-axis. At this point, [tex]\(y = 0\)[/tex].
Substitute [tex]\(y = 0\)[/tex] in the equation [tex]\(5x - 3y = 15\)[/tex]:
[tex]\[
5x - 3(0) = 15 \\
5x = 15 \\
x = \frac{15}{5} \\
x = 3
\][/tex]
So, the [tex]\(x\)[/tex]-intercept is [tex]\((3, 0)\)[/tex].
2. Find the [tex]\(y\)[/tex]-intercept:
The [tex]\(y\)[/tex]-intercept is the point where the line crosses the [tex]\(y\)[/tex]-axis. At this point, [tex]\(x = 0\)[/tex].
Substitute [tex]\(x = 0\)[/tex] in the equation:
[tex]\[
5(0) - 3y = 15 \\
-3y = 15 \\
y = \frac{15}{-3} \\
y = -5
\][/tex]
So, the [tex]\(y\)[/tex]-intercept is [tex]\((0, -5)\)[/tex].
3. Plot the intercepts:
On a coordinate plane:
- Mark the point [tex]\( (3, 0) \)[/tex] (which is the [tex]\(x\)[/tex]-intercept).
- Mark the point [tex]\( (0, -5) \)[/tex] (which is the [tex]\(y\)[/tex]-intercept).
4. Draw the line:
Using a ruler or a straight edge, draw a line through the points [tex]\((3, 0)\)[/tex] and [tex]\((0, -5)\)[/tex]. This line represents the graph of the equation [tex]\(5x - 3y = 15\)[/tex].
5. Label the graph:
- Label the line with its equation [tex]\(5x - 3y = 15\)[/tex].
- Clearly indicate the intercepts: [tex]\((3, 0)\)[/tex] and [tex]\((0, -5)\)[/tex].
By following these steps, you should have a correctly plotted graph of the equation [tex]\(5x - 3y = 15\)[/tex] with its [tex]\(x\)[/tex]- and [tex]\(y\)[/tex]-intercepts clearly marked.
