To determine the location of the [tex]\( y \)[/tex]-intercept of the linear function [tex]\( y = -5x - 7 \)[/tex], we follow these steps:
1. Understand the concept of [tex]\( y \)[/tex]-intercept:
- The [tex]\( y \)[/tex]-intercept of a linear function is the point where the line crosses the [tex]\( y \)[/tex]-axis.
- At the [tex]\( y \)[/tex]-intercept, the value of [tex]\( x \)[/tex] is always 0.
2. Substitute [tex]\( x = 0 \)[/tex] into the equation:
- We take the equation [tex]\( y = -5x - 7 \)[/tex] and substitute [tex]\( x \)[/tex] with 0 to find the value of [tex]\( y \)[/tex].
- Calculation:
[tex]\[
y = -5(0) - 7
\][/tex]
- This simplifies to:
[tex]\[
y = -7
\][/tex]
3. Identify the coordinates of the [tex]\( y \)[/tex]-intercept:
- The [tex]\( y \)[/tex]-intercept has the coordinates [tex]\( (x, y) \)[/tex].
- Since we substituted [tex]\( x = 0 \)[/tex] and found [tex]\( y = -7 \)[/tex], the [tex]\( y \)[/tex]-intercept will be at the point [tex]\( (0, -7) \)[/tex].
Therefore, the location of the [tex]\( y \)[/tex]-intercept of the function [tex]\( y = -5x - 7 \)[/tex] is:
[tex]\[
\boxed{(0, -7)}
\][/tex]
