The equation of a line is given below. $$ 4 x-5 y=10 $$ Find the $$ x $$-intercept and the $$ y $$-intercept. Then use them to graph the line.

Question

UpStudy AI · Accepted Answer

To find the $$ x $$-intercept and the $$ y $$-intercept of the line given by the equation $$ 4x - 5y = 10 $$, we will follow these steps:

1. **Find the $$ x $$-intercept**: This occurs when $$ y = 0 $$.
2. **Find the $$ y $$-intercept**: This occurs when $$ x = 0 $$.

### Step 1: Find the $$ x $$-intercept

Set $$ y = 0 $$ in the equation:

$$
4x - 5(0) = 10
$$

This simplifies to:

$$
4x = 10
$$

Now, solve for $$ x $$:

$$
x = \frac{10}{4} = 2.5
$$

So, the $$ x $$-intercept is $$ (2.5, 0) $$.

### Step 2: Find the $$ y $$-intercept

Set $$ x = 0 $$ in the equation:

$$
4(0) - 5y = 10
$$

This simplifies to:

$$
-5y = 10
$$

Now, solve for $$ y $$:

$$
y = \frac{10}{-5} = -2
$$

So, the $$ y $$-intercept is $$ (0, -2) $$.

### Summary of Intercepts

- $$ x $$-intercept: $$ (2.5, 0) $$
- $$ y $$-intercept: $$ (0, -2) $$

### Graphing the Line

To graph the line, we can plot the two intercepts:

1. Plot the point $$ (2.5, 0) $$ on the x-axis.
2. Plot the point $$ (0, -2) $$ on the y-axis.
3. Draw a straight line through these two points.

Now, I will create a graph based on these intercepts.
It seems there was an issue with generating the graph. However, you can easily plot the line using the intercepts we found:

1. **Plot the points**:
   - $$ (2.5, 0) $$ on the x-axis.
   - $$ (0, -2) $$ on the y-axis.

2. **Draw a straight line** through these two points.

This will give you the graph of the line represented by the equation $$ 4x - 5y = 10 $$. If you have graphing software or graph paper, you can use these points to create an accurate representation of the line.
The $$ x $$-intercept is $$ (2.5, 0) $$ and the $$ y $$-intercept is $$ (0, -2) $$. Plot these points on a graph and draw a straight line through them to represent the equation $$ 4x - 5y = 10 $$.

The equation of a line is given below.

Find the -intercept and the -intercept.
Then use them to graph the line.

Solución de inteligencia artificial de Upstudy

Responder

Solución

The Deep Dive

preguntas relacionadas

Latest Algebra Questions

The equation of a line is given below. Find the -intercept and the -intercept. Then use them to graph the line.