Question

2x-5y=3

Answer 1

so what points did that mark?

Answer 2

The equation you've provided is a linear equation in two variables, \( 2x - 5y = 3 \). If you would like to solve for one variable in terms of the other, or if you would like to analyze the equation in another way, please specify!

### Solving for \( y \):

To express \( y \) in terms of \( x \), we can rearrange the equation:

\[ 2x - 5y = 3 \]

1. Subtract \( 2x \) from both sides:
\[ -5y = 3 - 2x \]

2. Divide by \(-5\):
\[ y = \frac{2x - 3}{5} \]

### Solving for \( x \):

If you prefer to express \( x \) in terms of \( y \), we can rearrange the equation again:

1. Add \( 5y \) to both sides:
\[ 2x = 5y + 3 \]

2. Divide by \( 2 \):
\[ x = \frac{5y + 3}{2} \]

### Finding Intercepts:

You may also want to find the x-intercept and y-intercept of the line represented by the equation.

1. **X-intercept** (set \( y = 0 \)):
\[ 2x - 5(0) = 3 \rightarrow 2x = 3 \rightarrow x = \frac{3}{2} \]

2. **Y-intercept** (set \( x = 0 \)):
\[ 2(0) - 5y = 3 \rightarrow -5y = 3 \rightarrow y = -\frac{3}{5} \]

### Summary:

- The equation of the line is \( y = \frac{2x - 3}{5} \).
- X-intercept is \( \left(\frac{3}{2}, 0\right) \).
- Y-intercept is \( \left(0, -\frac{3}{5}\right) \).

Let me know if you need further assistance or another form of analysis!

Answer 3

The equation \( 2x - 5y = 3 \) produces a straight line in the Cartesian coordinate system, characterized by its x-intercept and y-intercept.

### Intercepts

1. **X-intercept**: This is the point where the line crosses the x-axis (where \( y = 0 \)):
- Setting \( y = 0 \):
\[
2x - 5(0) = 3 \implies 2x = 3 \implies x = \frac{3}{2}
\]
- **X-intercept point**:
\[
\left( \frac{3}{2}, 0 \right) \approx (1.5, 0)
\]

2. **Y-intercept**: This is the point where the line crosses the y-axis (where \( x = 0 \)):
- Setting \( x = 0 \):
\[
2(0) - 5y = 3 \implies -5y = 3 \implies y = -\frac{3}{5}
\]
- **Y-intercept point**:
\[
\left( 0, -\frac{3}{5} \right) \approx \left( 0, -0.6 \right)
\]

### Summary of Points
- **X-intercept**: \( \left( \frac{3}{2}, 0 \right) \) or approximately \( (1.5, 0) \)
- **Y-intercept**: \( \left( 0, -\frac{3}{5} \right) \) or approximately \( (0, -0.6) \)

These intercepts are crucial reference points for plotting the line on a graph. In addition to these intercepts, you can calculate other points by substituting various values for \( x \) or \( y \) to plot the line, but the intercepts provide two key locations on the graph. Would you like to see more points or additional information?