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:
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).