choose all the points that lie on the line 7x - y + 3 = 0
A - (3,24)
B - (-4,-24)
C - (0,3)
D - (2,17)

To determine which points lie on the line defined by the equation \(7x - y + 3 = 0\), we will substitute the coordinates of each point into the equation. If the equation holds true (i.e., both sides are equal), then the point lies on the line.

The line equation is:
\[
7x - y + 3 = 0 \quad \Rightarrow \quad 7x - y = -3
\]

Let's check each point:

- **A (3, 24):**
\[
7(3) - 24 = 21 - 24 = -3 \quad \text{(True, this point lies on the line)}
\]

- **B (-4, -24):**
\[
7(-4) - (-24) = -28 + 24 = -4 \quad \text{(False, this point does not lie on the line)}
\]

- **C (0, 3):**
\[
7(0) - 3 = 0 - 3 = -3 \quad \text{(True, this point lies on the line)}
\]

- **D (2, 17):**
\[
7(2) - 17 = 14 - 17 = -3 \quad \text{(True, this point lies on the line)}
\]

### Conclusion:
The points that lie on the line are:
- **A (3, 24)**
- **C (0, 3)**
- **D (2, 17)**

Would you like further details or clarifications?

Here are 5 related questions for practice:
1. What is the slope of the line \(7x - y + 3 = 0\)?
2. How do you find the y-intercept of the line \(7x - y + 3 = 0\)?
3. Can you find a point on the line \(7x - y + 3 = 0\) when \(x = 5\)?
4. How would you rewrite \(7x - y + 3 = 0\) in slope-intercept form?
5. What is the equation of a line parallel to \(7x - y + 3 = 0\)?

**Tip**: Always check whether a point lies on a line by substituting its coordinates into the line equation.

This page provides a detailed solution to the problem of determining which points lie on the line 7x - y + 3 = 0. Using substitution, we evaluate whether points A (3, 24), B (-4, -24), C (0, 3), and D (2, 17) satisfy the line equation. Ideal for students in Grades 8-10.

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