The slope-intercept form of a linear equation is:

$y = mx + b$

Here:

• $m = 4$ (the given slope)
• The line passes through the point $(-2, 1)$, which we use to find $b$ (the y-intercept).

Step 1: Substitute the given values into the slope-intercept form

Substitute $x = -2$, $y = 1$, and $m = 4$ into $y = mx + b$:

$1 = 4(-2) + b$

Step 2: Solve for $b$

$1 = -8 + b$ $b = 9$

Step 3: Write the equation

Substitute $m = 4$ and $b = 9$ into $y = mx + b$:

$y = 4x + 9$

Final Answer:

The equation of the line is: $y = 4x + 9$

Would you like further details or clarification? Here are some related questions to consider:

1. How is the slope-intercept form derived from two points?
2. Can this method be applied to vertical or horizontal lines?
3. How does the slope influence the steepness of the line?
4. What happens to the equation if the slope is negative?
5. How can you verify the accuracy of the equation with another point?

Tip: Always double-check by substituting the point back into the equation to confirm its accuracy.