Option C (Same as Option D)
Explanation:
Option C and D are the same, so I'll assume you made a mistake when writing this question. However, let's figure out which of the following equations has a slope of -2 and passes through the point (2,3):
A. y = -2x + 6
B. y - 3 = -2(x + 2)
C. y = -2x + 7
All these equations have a slope of -2.
FROM OPTION A:
[tex]Recall \ our \ point \ is \ (2,3), \ so: \\ \\ x=2 \\ \\ y=3 \\ \\ Substituting \ into \ the \ equation: \\ \\ 3=-2(2)+6 \\ \\ 3=-4+6 \\ \\ 3=2 \ False![/tex]
Since [tex]3\neq 2[/tex] then the line doesn't pass through the point (2, 3)
FROM OPTION B:
[tex]Recall \ our \ point \ is \ (2,3), \ so: \\ \\ x=2 \\ \\ y=3 \\ \\ Substituting \ into \ the \ equation: \\ \\ 3-3=-2((2)+2) \\ \\ 0=-2(4) \\ \\ 0=-8 \ False![/tex]
Since [tex]0\neq -8[/tex] then the line doesn't pass through the point (2, 3)
FROM OPTION C:
[tex]Recall \ our \ point \ is \ (2,3), \ so: \\ \\ x=2 \\ \\ y=3 \\ \\ Substituting \ into \ the \ equation: \\ \\ 3=-2(2)+7 \\ \\ 3=-4+7 \\ \\ 3=3 \ True![/tex]
Since [tex]3\neq 3[/tex] then the line passes through the point (2, 3)
Finally, the equation that has a slope of -2 and passes through the point (2,3) is Option C (Same as Option D)
Learn more:
x and y intercepts of a line: https://brainly.com/question/13770925#
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