To find the [tex]\( y \)[/tex]-intercept of the line given by the equation [tex]\( y = 5x - 21 \)[/tex], we need to determine the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is [tex]\( 0 \)[/tex]. The [tex]\( y \)[/tex]-intercept is the point where the line crosses the [tex]\( y \)[/tex]-axis.
Here’s a step-by-step solution:
1. Start with the given equation of the line:
[tex]\[
y = 5x - 21
\][/tex]
2. Substitute [tex]\( x = 0 \)[/tex] into the equation to find the [tex]\( y \)[/tex]-intercept:
[tex]\[
y = 5(0) - 21
\][/tex]
3. Simplify the equation:
[tex]\[
y = 0 - 21
\][/tex]
[tex]\[
y = -21
\][/tex]
So, the [tex]\( y \)[/tex]-intercept is the point [tex]\((0, -21)\)[/tex].
Given the options:
A. [tex]\((0, -21)\)[/tex]
B. [tex]\((0, 21)\)[/tex]
C. [tex]\((0, 5)\)[/tex]
D. [tex]\((0, -5)\)[/tex]
The correct answer is:
A. [tex]\((0, -21)\)[/tex]
