To determine the [tex]\(x\)[/tex]-intercept of a line, we need to find the point where the line crosses the [tex]\(x\)[/tex]-axis. At this point, the value of [tex]\(y\)[/tex] is 0.
The general equation of a line can be written as:
[tex]\[ y = mx + c \][/tex]
where [tex]\(m\)[/tex] is the gradient and [tex]\(c\)[/tex] is the [tex]\(y\)[/tex]-intercept.
Given:
- The gradient ([tex]\(m\)[/tex]) is -2.
- The [tex]\(y\)[/tex]-intercept ([tex]\(c\)[/tex]) is 5.
We substitute these values into the equation of the line:
[tex]\[ y = -2x + 5 \][/tex]
To find the [tex]\(x\)[/tex]-intercept, set [tex]\(y = 0\)[/tex] because at the [tex]\(x\)[/tex]-intercept, the line crosses the [tex]\(x\)[/tex]-axis where [tex]\(y\)[/tex] is zero:
[tex]\[ 0 = -2x + 5 \][/tex]
Now, solve for [tex]\(x\)[/tex]:
[tex]\[ -2x + 5 = 0 \][/tex]
[tex]\[ -2x = -5 \][/tex]
[tex]\[ x = \frac{-5}{-2} \][/tex]
[tex]\[ x = \frac{5}{2} \][/tex]
Therefore, the [tex]\(x\)[/tex]-intercept of the line is [tex]\( \frac{5}{2} \)[/tex], which is approximately 2.5.
