Find the equation (in terms of x) of the line through the points (-4,6) and (1,-4).

y=

To find the equation of the line passing through the points \((-4, 6)\) and \((1, -4)\), we can use the point-slope form of the equation of a line:

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

where \(m\) is the slope of the line, and \((x_1, y_1)\) is one of the points on the line.

### Step 1: Find the Slope (\(m\))

The slope \(m\) is calculated as:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using the points \((-4, 6)\) and \((1, -4)\):

\[
m = \frac{-4 - 6}{1 - (-4)} = \frac{-10}{5} = -2
\]

### Step 2: Use the Point-Slope Form

Now, substitute \(m = -2\) and one of the points, say \((1, -4)\), into the point-slope form:

\[
y - (-4) = -2(x - 1)
\]

Simplify the equation:

\[
y + 4 = -2(x - 1)
\]

### Step 3: Simplify to the Slope-Intercept Form (\(y = mx + b\))

Expand and simplify:

\[
y + 4 = -2x + 2
\]

Subtract 4 from both sides:

\[
y = -2x - 2
\]

So, the equation of the line in terms of \(x\) is:

\[
\boxed{y = -2x - 2}
\]

Would you like more details or have any questions?

Here are some related questions to explore:
1. How would you find the equation of a line given its slope and one point?
2. What is the general form of the equation of a line?
3. How do you determine if two lines are parallel or perpendicular?
4. Can you find the y-intercept of a line given two points?
5. How does changing the slope affect the steepness of a line?

**Tip:** When calculating the slope between two points, remember that a negative slope means the line is decreasing (going downwards) as it moves from left to right.

Find the equation (in terms of x) of the line through the points (-4,6) and (1,-4).

Find the equation of the line passing through the points (-4,6) and (1,-4) with a detailed step-by-step solution. Learn how to use the slope formula, point-slope form, and slope-intercept form. This problem is ideal for students in Grades 8-10.

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