To write the linear equation for the line passing through the points (-3, 7) and (1, -1), we can start by calculating the slope \( m \) using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let’s assign the points as follows:
- \((x_1, y_1) = (-3, 7)\)
- \((x_2, y_2) = (1, -1)\)
Now, we can plug in the values into the slope formula:
\[ m = \frac{-1 - 7}{1 - (-3)} \] \[ m = \frac{-8}{1 + 3} \] \[ m = \frac{-8}{4} = -2 \]
Next, we’ll use the point-slope form of the equation of the line, which is:
\[ y - y_1 = m(x - x_1) \]
Using \((x_1, y_1) = (-3, 7)\) and \(m = -2\), we can substitute these values into the equation:
\[ y - 7 = -2(x - (-3)) \] \[ y - 7 = -2(x + 3) \]
This is the linear equation in point-slope form. To express it in slope-intercept form (y = mx + b), we can simplify:
\[ y - 7 = -2x - 6 \] \[ y = -2x - 6 + 7 \] \[ y = -2x + 1 \]
Thus, the equation of the line in slope-intercept form is:
\[ y = -2x + 1 \]