To find the [tex]\( x \)[/tex]-intercept of a line given its gradient (slope) and [tex]\( y \)[/tex]-intercept, we can use the equation of the line in its slope-intercept form:
[tex]\[ y = mx + b \][/tex]
where:
- [tex]\( m \)[/tex] is the gradient (slope) of the line,
- [tex]\( b \)[/tex] is the [tex]\( y \)[/tex]-intercept.
Given:
- The gradient [tex]\( m = -2 \)[/tex]
- The [tex]\( y \)[/tex]-intercept [tex]\( b = 5 \)[/tex]
The equation of the line can be written as:
[tex]\[ y = -2x + 5 \][/tex]
At the [tex]\( x \)[/tex]-intercept, the value of [tex]\( y \)[/tex] is 0. So, we set [tex]\( y = 0 \)[/tex] and solve for [tex]\( x \)[/tex]:
[tex]\[ 0 = -2x + 5 \][/tex]
To isolate [tex]\( x \)[/tex], we follow these steps:
1. Add [tex]\( 2x \)[/tex] to both sides of the equation:
[tex]\[ 2x = 5 \][/tex]
2. Divide both sides by 2:
[tex]\[ x = \frac{5}{2} \][/tex]
Hence, the [tex]\( x \)[/tex]-intercept of the line is [tex]\( \boxed{2.5} \)[/tex].
