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To solve this, we need to find the equation of the line passing through the points \((0, 1)\) and \((3, 7)\) and then determine which additional points lie on that line.

### Step 1: Find the slope of the line
The slope \(m\) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

For the points \((0, 1)\) and \((3, 7)\):

\[
m = \frac{7 - 1}{3 - 0} = \frac{6}{3} = 2
\]

### Step 2: Use the slope-intercept form
The equation of a line in slope-intercept form is:

\[
y = mx + b
\]

Where:
- \(m\) is the slope
- \(b\) is the y-intercept

Since the line passes through \((0, 1)\), the y-intercept \(b = 1\). Therefore, the equation of the line is:

\[
y = 2x + 1
\]

### Step 3: Determine which points lie on the line
Now, we can check if any given point lies on this line by substituting its coordinates \((x, y)\) into the equation \(y = 2x + 1\). Do you have the points that we need to test?

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Would you like a detailed breakdown or any additional help with the next steps?

Here are some related questions:
1. How do you determine the equation of a line passing through two given points?
2. What is the significance of the slope in the equation of a line?
3. How can you verify if a point lies on a specific line?
4. How does changing the slope affect the steepness of the line?
5. How can you find the x-intercept of a line from its equation?

**Tip:** When working with linear equations, always simplify the slope first to avoid calculation mistakes.

A line passes through the point (0, 1) and (3, 7). Which of these points also lies on the line?

Learn how to determine if a point lies on the line passing through the points (0, 1) and (3, 7). This problem explores the slope formula and slope-intercept form of a linear equation. Suitable for students in Grades 8-10.

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