Slope 7​, passing through left parenthesis (-2,1)

To find the equation of a line with a given slope and a point it passes through, we use the **point-slope form** of the equation of a line:

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

Where:
- \(m\) is the slope,
- \((x_1, y_1)\) is a point on the line.

Here:
- Slope \(m = 7\),
- Point \((x_1, y_1) = (-2, 1)\).

Substituting these values into the formula:

\[
y - 1 = 7(x + 2)
\]

Now, let's simplify this to get the equation in slope-intercept form:

\[
y - 1 = 7x + 14
\]

Add 1 to both sides:

\[
y = 7x + 15
\]

So, the equation of the line is:

\[
y = 7x + 15
\]

Would you like further details or have any questions?

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Here are 5 questions related to this topic:

1. How do you find the equation of a line given two points instead of slope?
2. What is the difference between point-slope and slope-intercept forms?
3. How do you interpret the y-intercept in a linear equation?
4. How would the equation change if the slope were negative?
5. Can you graph the equation of a line with only the slope and a point?

**Tip:** Always double-check the slope and point before plugging them into the formula to avoid errors!

Learn how to find the equation of a line with a slope of 7 passing through the point (-2, 1). This solution uses the point-slope form and simplifies it to slope-intercept form, covering key concepts in linear equations. Suitable for Grades 8-10.

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