Question

(2,-9) (-1,6) The slope y intercept and equation

Answer 1

To find the slope, y-intercept, and equation of the line passing through the points (2, -9) and (-1, 6), we can use the following steps:

### Step 1: Calculate the Slope (m)
The slope \( m \) is given by the formula:

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

Where \( (x_1, y_1) = (2, -9) \) and \( (x_2, y_2) = (-1, 6) \).

Substituting in the values, we get:

\[
m = \frac{6 - (-9)}{-1 - 2} = \frac{6 + 9}{-3} = \frac{15}{-3} = -5
\]

### Step 2: Use Point-Slope Form to Find the Equation
Now that we have the slope, we can use point-slope form to find the equation of the line. The point-slope form is given by:

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

Using one of the points, let's use (2, -9):

\[
y - (-9) = -5(x - 2)
\]

This simplifies to:

\[
y + 9 = -5x + 10
\]

Subtracting 9 from both sides, we get:

\[
y = -5x + 1
\]

### Step 3: Identify the y-Intercept (b)
The equation is in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. In our case, the y-intercept \( b \) is \( 1 \).

### Summary
- Slope (m): \(-5\)
- Y-Intercept (b): \(1\)
- Equation of the line: \(y = -5x + 1\)