To find the [tex]$y$[/tex]-intercept of a line given by the equation in the form [tex]\( y = mx + b \)[/tex], we need to identify the value of [tex]\( y \)[/tex] when [tex]\( x \)[/tex] is 0. The [tex]$y$[/tex]-intercept is the point at which the line crosses the [tex]$y$[/tex]-axis, and this occurs where [tex]\( x = 0 \)[/tex].
Given the equation:
[tex]\[ y = 8x + 75 \][/tex]
Let's determine the [tex]$y$[/tex]-intercept by setting [tex]\( x = 0 \)[/tex]:
[tex]\[ y = 8(0) + 75 \][/tex]
[tex]\[ y = 0 + 75 \][/tex]
[tex]\[ y = 75 \][/tex]
Therefore, when [tex]\( x = 0 \)[/tex], [tex]\( y \)[/tex] is 75. Hence, the [tex]$y$[/tex]-intercept of the line is:
[tex]\[ (0, 75) \][/tex]
The correct answer is:
C. [tex]\((0, 75)\)[/tex]
