To determine the y-intercept of the equation [tex]\(y = -4x - 7\)[/tex], we need to understand what the y-intercept represents. The y-intercept is the point where the graph of the equation crosses the y-axis. At the y-axis, the value of [tex]\(x\)[/tex] is always [tex]\(0\)[/tex].
So, to find the y-intercept, we set [tex]\(x\)[/tex] to [tex]\(0\)[/tex] in the equation:
[tex]\[ y = -4x - 7 \][/tex]
Substituting [tex]\(x = 0\)[/tex] into the equation:
[tex]\[ y = -4(0) - 7 \][/tex]
[tex]\[ y = -7 \][/tex]
Therefore, when [tex]\(x = 0\)[/tex], [tex]\(y = -7\)[/tex].
The ordered pair for the y-intercept is [tex]\((0, -7)\)[/tex].
Considering the given options:
A. [tex]\((-4, 0)\)[/tex]
B. [tex]\((-7, 0)\)[/tex]
C. [tex]\((0, -7)\)[/tex]
D. [tex]\((0, -4)\)[/tex]
The ordered pair that represents the y-intercept of the graph of the equation [tex]\(y = -4x - 7\)[/tex] is [tex]\((0, -7)\)[/tex], which corresponds to option C.
