Question

URGENT!! A line has slope -3 and (4,-1) is a point on this line. Which, if any, of the following points are also on this line?

Point A is (4, 0)

Point B is (3,2)

Point C is (5, -4)

Answer 1

To determine which of the given points are on the line with a slope of -3 passing through the point (4, -1), you can use the point-slope form of the equation for a line:

\[y - y_1 = m(x - x_1)\]

where (x1, y1) is a point on the line, m is the slope, and (x, y) are the coordinates of the other points.

For the point (4, 0) (Point A):
\[y - (-1) = -3(x - 4)\]
\[y + 1 = -3x + 12\]
\[y = -3x + 11\]

Now, let's check the other points:

Point B (3, 2):
\[2 - (-1) = -3(3 - 4)\]
\[3 = 3\]

The equation does not hold for Point B, so Point B is not on the line.

Point C (5, -4):
\[-4 - (-1) = -3(5 - 4)\]
\[-3 = -3\]

The equation holds for Point C, so Point C is on the line.

In summary:
- Point A (4, 0) is not on the line.
- Point B (3, 2) is not on the line.
- Point C (5, -4) is on the line.

Answer 2

The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept. Given a point (x1, y1) on the line, the equation becomes y - y1 = m(x - x1).

Given that the slope m is -3 and (4,-1) is a point on the line, we can substitute these values into the equation to get y - (-1) = -3(x - 4). Simplifying this gives us y = -3x + 11.

Now we can check which of the given points satisfy this equation:

Point A (4, 0): Substituting x = 4 and y = 0 into the equation gives us 0 = -3*4 + 11, which simplifies to 0 = -1. Since this is not true, Point A is not on the line.

Point B (3,2): Substituting x = 3 and y = 2 into the equation gives us 2 = -3*3 + 11, which simplifies to 2 = 2. Since this is true, Point B is on the line.

Point C (5, -4): Substituting x = 5 and y = -4 into the equation gives us -4 = -3*5 + 11, which simplifies to -4 = -4. Since this is true, Point C is on the line.

So, among the given points, Points B and C are on the line.