To find the equation of the line passing through the points (-1, -6) and (4, 4), follow these steps:

Step 1: Find the Slope (m)

The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Substituting the given points $(-1, -6)$ and $(4, 4)$:

$m = \frac{4 - (-6)}{4 - (-1)} = \frac{4 + 6}{4 + 1} = \frac{10}{5} = 2$

Step 2: Use the Point-Slope Form

The point-slope formula is:

$y - y_1 = m(x - x_1)$

Using $m = 2$ and $(x_1, y_1) = (-1, -6)$:

$y - (-6) = 2(x - (-1))$

$y + 6 = 2(x + 1)$

Step 3: Convert to Slope-Intercept Form (y = mx + b)

Expanding:

$y + 6 = 2x + 2$

$y = 2x + 2 - 6$

$y = 2x - 4$

Final Answer:

$y = 2x - 4$

Would you like a step-by-step graph of this line? Let me know if you have any questions!

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Related Questions:

1. How do you find the equation of a line given the slope and one point?
2. What is the equation of a line perpendicular to $y = 2x - 4$ passing through (3,2)?
3. How do you find the x-intercept and y-intercept of $y = 2x - 4$?
4. How do you convert an equation from point-slope form to standard form?
5. What are parallel lines, and how do you find an equation parallel to $y = 2x - 4$?

Tip:

The y-intercept of a line is found by setting $x = 0$. For $y = 2x - 4$, the y-intercept is $-4$.