Question

Find the intercepts and then use them to graph the equation.
5xplusyequals10

Answer 1

To find the intercepts of the equation \(5x + y = 10\), we can calculate both the x-intercept and the y-intercept.

### Finding the x-intercept:
To find the x-intercept, set \(y = 0\) in the equation:

\[
5x + 0 = 10
\]

This simplifies to:

\[
5x = 10
\]

Dividing both sides by 5 gives:

\[
x = 2
\]

So the x-intercept is \((2, 0)\).

### Finding the y-intercept:
To find the y-intercept, set \(x = 0\) in the equation:

\[
5(0) + y = 10
\]

This simplifies to:

\[
y = 10
\]

So the y-intercept is \((0, 10)\).

### Summary of Intercepts:
- x-intercept: \((2, 0)\)
- y-intercept: \((0, 10)\)

### Graphing the Equation:
To graph the equation using the intercepts:

1. Plot the x-intercept \((2, 0)\) on the graph.
2. Plot the y-intercept \((0, 10)\) on the graph.
3. Draw a line through these two points.

### The Graph:
The line will slope downwards from left to right because the equation is linear.

Here’s a quick sketch of the graph:

- The x-axis can go from \(0\) to \(3\) (displaying the x-intercept)
- The y-axis can go from \(0\) to \(10\) (displaying the y-intercept)

You will end up with a straight line that intersects the x-axis at \((2,0)\) and the y-axis at \((0,10)\).