Which can be the first step in finding the equation of the line that passes through the points (5, negative 4) and (negative 1, 8) in slope-intercept form?
Calculate StartFraction 8 minus (negative 4) Over negative 1 minus 5 EndFraction = StartFraction 12 Over negative 6 EndFraction = negative 2..
Calculate StartFraction negative 1 minus 5 Over 8 minus (negative 4) EndFraction = StartFraction negative 6 Over 12 EndFraction = negative one-half..
Find that the point at which the line intersects with the line y = 0 is (3, 0).
Find that the point at which the line intersects with the line x = y is (2, 2).

The first step in finding the equation of a line that passes through two points, such as \((5, -4)\) and \((-1, 8)\), is to calculate the slope (\(m\)) using the slope formula:

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

Here, \((x_1, y_1) = (5, -4)\) and \((x_2, y_2) = (-1, 8)\).

### Step-by-step calculation of the slope:

1. Subtract the \(y\)-coordinates: 
   \[
   8 - (-4) = 8 + 4 = 12
   \]

2. Subtract the \(x\)-coordinates:
   \[
   -1 - 5 = -6
   \]

3. Now, compute the slope:
   \[
   m = \frac{12}{-6} = -2
   \]

So, the slope of the line is \(m = -2\).

### Next Step: Find the equation in slope-intercept form (\(y = mx + b\)).

To find the \(y\)-intercept (\(b\)), substitute one of the points, say \((5, -4)\), and the slope \(m = -2\) into the equation \(y = mx + b\):

1. Substitute \(x = 5\), \(y = -4\), and \(m = -2\):
   \[
   -4 = -2(5) + b
   \]

2. Simplify and solve for \(b\):
   \[
   -4 = -10 + b
   \]
   \[
   b = -4 + 10 = 6
   \]

### Final Equation:

The equation of the line is:
\[
y = -2x + 6
\]

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Let me know if you would like to go into more detail on any of the steps or explore other related problems. Here are some follow-up questions:

1. What is the significance of the slope in a line's equation?
2. How would the equation change if the slope were positive?
3. Can you verify the equation by substituting the other point \((-1, 8)\)?
4. How can we find the intersection point of this line with another line, say \(y = x\)?
5. How would you calculate the distance between the two points \((5, -4)\) and \((-1, 8)\)?

**Tip:** When finding the slope between two points, always double-check the order of subtraction to avoid sign mistakes.

Which can be the first step in finding the equation of the line that passes through the points (5, -4) and (-1, 8) in slope-intercept form? Calculate 8 minus (-4) over -1 minus 5 equals 12 over -6 equals -2. Calculate -1 minus 5 over 8 minus (-4) equals -6 over 12 equals -1/2. Find that the point at which the line intersects with the line y = 0 is (3, 0). Find that the point at which the line intersects with the line x = y is (2, 2).

Learn how to find the equation of a line that passes through the points (5, -4) and (-1, 8) in slope-intercept form. This step-by-step solution involves calculating the slope and determining the y-intercept. Ideal for students in Grades 8-10 studying linear equations.

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