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SOMEONE HELP CONFIRM PLEASE (4,-3),y=3x-5

User Sambatyon
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1 Answer

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The correct statements are:

2. The line through (4, -3) has a slope of 3.

4. The line y = 3x - 5 is parallel.

Let's analyze each statement:

1. The point (4, -3) lies on the line y = 3x - 5.

To check this, substitute x = 4 into the equation:
\( y = 3(4) - 5 = 12 - 5 = 7 \).Therefore, the point (4, -3) does not lie on the line y = 3x - 5. This statement is false.

2. The slope of the line passing through the point (4, -3) is 3

The slope of a line can be determined from its equation in the form y = mx + b, where m is the slope. In the given line y = 3x - 5, the slope is 3. Therefore, this statement is true.

3. The y-intercept of the line passing through the point (4, -3) is -5.

To find the y-intercept, we can substitute x = 0 into the equation. For the line passing through (4, -3), the equation becomes y = 3(0) + b , where b is the y-intercept. Solving for b, we find b = -3 . Therefore, this statement is false.

4. The line y = 3x - 5 is parallel to the line passing through the point (4, -3).

Since the line passing through (4, -3) has a slope of 3, and the given line y = 3x - 5 also has a slope of 3, the two lines are parallel. This statement is true.

In summary, statements 2 and 4 are true, while statements 1 and 3 are false. The point (4, -3) is not on the given line, and the y-intercept of the line passing through (4, -3) is not -5. However, the slopes of the two lines are equal, making them parallel.

Question:

We are given a point (4, -3) and a line represented by the equation y = 3x - 5. Which of the following statements is true about their relationship?

1. The point (4, -3) lies on the line y = 3x - 5.

2. The slope of the line passing through the point (4, -3) is 3.

3. The y-intercept of the line passing through the point (4, -3) is -5.

4. The line y = 3x - 5 is parallel to the line passing through the point (4, -3).

User PIXP
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