To graph the line described by the equation [tex]\(5x + 4y + 20 = 0\)[/tex], you can find and use the x-intercept and y-intercept. Here are the steps to do that:
1. Find the x-intercept:
The x-intercept occurs where the line crosses the x-axis, which is when [tex]\(y = 0\)[/tex].
Substitute [tex]\(y = 0\)[/tex] into the equation:
[tex]\[
5x + 4(0) + 20 = 0
\][/tex]
Simplify to find [tex]\(x\)[/tex]:
[tex]\[
5x + 20 = 0 \implies 5x = -20 \implies x = -4
\][/tex]
So, the x-intercept is at [tex]\((-4, 0)\)[/tex].
2. Find the y-intercept:
The y-intercept occurs where the line crosses the y-axis, which is when [tex]\(x = 0\)[/tex].
Substitute [tex]\(x = 0\)[/tex] into the equation:
[tex]\[
5(0) + 4y + 20 = 0
\][/tex]
Simplify to find [tex]\(y\)[/tex]:
[tex]\[
4y + 20 = 0 \implies 4y = -20 \implies y = -5
\][/tex]
So, the y-intercept is at [tex]\((0, -5)\)[/tex].
3. Graph the line:
- Plot the x-intercept [tex]\((-4, 0)\)[/tex] on the graph.
- Plot the y-intercept [tex]\((0, -5)\)[/tex] on the graph.
- Draw a straight line through the two points. This line represents the equation [tex]\(5x + 4y + 20 = 0\)[/tex].
The x-intercept and y-intercept provide two key points that determine the line. Connecting these points with a straight edge will give you the accurate graph of the equation.
