Question

Select the coordinates that are on a line parallel to

y=-3x-9 and goes through (3,2)

There are two

a
(2,5)

b
(-1,10)

c
(1,8)

d
(8,11)

Answer 1

To find the coordinates that are on a line parallel to \( y = -3x - 9 \) and goes through the point \( (3, 2) \), we need to first identify the slope of the given line.

The line \( y = -3x - 9 \) has a slope of \( -3 \). A parallel line will have the same slope.

We can express the equation of the new line that passes through the point \( (3, 2) \) using the point-slope form of the equation of a line:

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

Where \( (x_1, y_1) \) is the point and \( m \) is the slope. Plugging in our values:

\[
y - 2 = -3(x - 3)
\]

Now, simplifying this equation:

\[
y - 2 = -3x + 9
\]
\[
y = -3x + 11
\]

Now we have the equation of the line parallel to the original line and passing through the point \( (3, 2) \). We can now determine which of the given points lie on this new line by plugging in the x-coordinates and checking if the resulting y-coordinates match.

1. **For (2, 5)**:
\[
y = -3(2) + 11 = -6 + 11 = 5 \quad \text{(Correct)}
\]

2. **For (-1, 10)**:
\[
y = -3(-1) + 11 = 3 + 11 = 14 \quad \text{(Incorrect)}
\]

3. **For (1, 8)**:
\[
y = -3(1) + 11 = -3 + 11 = 8 \quad \text{(Correct)}
\]

4. **For (8, 11)**:
\[
y = -3(8) + 11 = -24 + 11 = -13 \quad \text{(Incorrect)}
\]

The points that lie on the line parallel to \( y = -3x - 9 \) and passing through \( (3, 2) \) are:

- (2, 5)
- (1, 8)

Thus, the correct answers are **a** (2, 5) and **c** (1, 8).