To determine at which point the line \( 5x + 3y = 10 \) meets the \( x \)-axis, we need to find the \( x \)-intercept of the line.
### Finding the \( x \)-intercept
The \( x \)-intercept is the point where the line crosses the \( x \)-axis. At this point, the \( y \)-coordinate is 0. Let's substitute \( y = 0 \) into the equation of the line and solve for \( x \):
[tex]\[ 5x + 3y = 10 \][/tex]
[tex]\[ 5x + 3(0) = 10 \][/tex]
[tex]\[ 5x = 10 \][/tex]
[tex]\[ x = \frac{10}{5} \][/tex]
[tex]\[ x = 2 \][/tex]
So the \( x \)-intercept of the line \( 5x + 3y = 10 \) is at the point \( (2, 0) \).
### Choosing the correct option
Among the given options:
- (a) \( (0, 3) \)
- (b) \( (3, 0) \)
- (c) \( (2, 0) \)
- (d) \( (0, 2) \)
The correct point where the line meets the \( x \)-axis is \( (2, 0) \).
### Conclusion
Therefore, the correct option is:
(c) [tex]\( (2, 0) \)[/tex]
