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?

---

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!