https://file.aiquickdraw.com/mathbot/file/1728939892638yc6dwxc6.jpg

The image contains a vertically oriented mathematical text. Here is the transcription:

**"...qui a un taux de variation de 5 et qui passe par (0, 1)."**

Translation from French:
"...which has a rate of change of 5 and passes through (0, 1)."

This likely refers to the equation of a **linear function** with a slope (rate of change) of 5 and passing through the point \((0, 1)\). The general form for a linear equation is:

\[
y = mx + b
\]

where \(m\) is the slope and \(b\) is the y-intercept. In this case:
- \(m = 5\)
- The line passes through \((0, 1)\), meaning the y-intercept \(b = 1\).

Thus, the equation of the line is:

\[
y = 5x + 1
\]

Would you like further details on this solution?

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Here are 5 follow-up questions to deepen your understanding:
1. How do you find the slope of a line given two points?
2. What does the slope of a line represent in real-world problems?
3. How do you interpret the y-intercept in the context of this problem?
4. How would the equation change if the slope were negative?
5. How can we verify that the point \((0, 1)\) lies on the equation \(y = 5x + 1\)?

**Tip:** Always verify that given points satisfy the equation by substituting them back into it.

What is the equation of the line which has a rate of change of 5 and passes through (0, 1)?

Learn how to find the equation of a line that has a slope of 5 and passes through the point (0, 1). This problem covers the slope-intercept form y = mx + b and basic algebraic principles. Suitable for students in Grades 8-10.

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