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What is the [tex]$y$[/tex]-intercept of the line given by the equation [tex]$y = 8x + 75$[/tex]?
A. [tex]$(0, -75)$[/tex] B. [tex]$(0, 8)$[/tex] C. [tex]$(0, 75)$[/tex] D. [tex]$(0, -8)$[/tex]
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]
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