Question

Which of the following equations has a slope of -2 and passes through the point (2,3)?

Answer 1

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:

$Recall \ our \ point \ is \ (2,3), \ so: \\ \\ x=2 \\ \\ y=3 \\ \\ Substituting \ into \ the \ equation: \\ \\ 3=-2(2)+6 \\ \\ 3=-4+6 \\ \\ 3=2 \ False!$

Since $3\neq 2$ then the line doesn't pass through the point (2, 3)

FROM OPTION B:

$Recall \ our \ point \ is \ (2,3), \ so: \\ \\ x=2 \\ \\ y=3 \\ \\ Substituting \ into \ the \ equation: \\ \\ 3-3=-2((2)+2) \\ \\ 0=-2(4) \\ \\ 0=-8 \ False!$

Since $0\neq -8$ then the line doesn't pass through the point (2, 3)

FROM OPTION C:

$Recall \ our \ point \ is \ (2,3), \ so: \\ \\ x=2 \\ \\ y=3 \\ \\ Substituting \ into \ the \ equation: \\ \\ 3=-2(2)+7 \\ \\ 3=-4+7 \\ \\ 3=3 \ True!$

Since $3\neq 3$ 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: brainly.com/question/13770925#

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