Question

Line P passes through the points (2, 9) and (4, 13). Line Q passes through the points (1, -13) and (3, -19).

Select a number for each blank to make the sentence true.

Answer 1

To find the equations of lines P and Q, we start by calculating their slopes and then use the point-slope formula to express each line.

### For Line P (points (2, 9) and (4, 13)):

1. **Calculate the slope (m)**:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{13 - 9}{4 - 2} = \frac{4}{2} = 2
\]

2. **Use the point-slope formula**: \( y - y_1 = m(x - x_1) \).
Using point (2, 9):
\[
y - 9 = 2(x - 2)
\]
Distributing the 2:
\[
y - 9 = 2x - 4
\]
So,
\[
y = 2x + 5
\]

### For Line Q (points (1, -13) and (3, -19)):

1. **Calculate the slope (m)**:
\[
m = \frac{-19 - (-13)}{3 - 1} = \frac{-19 + 13}{3 - 1} = \frac{-6}{2} = -3
\]

2. **Use the point-slope formula**:
Using point (1, -13):
\[
y - (-13) = -3(x - 1)
\]
This simplifies to:
\[
y + 13 = -3(x - 1)
\]
Distributing the -3:
\[
y + 13 = -3x + 3
\]
Therefore,
\[
y = -3x - 10
\]

### Summary of the Equations:

- The equation of Line P is \( y = 2x + 5 \)
- The equation of Line Q is \( y = -3x - 10 \)

Now we can fill in the blanks based on our findings:

1. For Line P's slope: **2**
2. For Line Q's slope: **-3**

So, the filled sentences would read: "The slope of Line P is **2** and the slope of Line Q is **-3**."