To find the equation of the line in slope-intercept form (\(y = mx + b\)), we'll start by calculating the slope (\(m\)) using the two points given: \((-4, -1)\) and \( (3, -2)\).
The slope formula is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \((x_1, y_1) = (-4, -1)\) and \((x_2, y_2) = (3, -2)\).
Calculating the slope:
\[ m = \frac{-2 - (-1)}{3 - (-4)} = \frac{-2 + 1}{3 + 4} = \frac{-1}{7} \]
Now that we have the slope \(m = -\frac{1}{7}\), we can use one of the points to find the y-intercept \(b\). We'll use the point \((3, -2)\).
Using the slope-intercept form:
\[ y = mx + b \]
Substituting \(m\) and the point \((3, -2)\):
\[ -2 = -\frac{1}{7} \cdot 3 + b \]
Calculating:
\[ -2 = -\frac{3}{7} + b \]
Now, isolate \(b\):
\[ b = -2 + \frac{3}{7} \]
To combine, convert \(-2\) to a fraction with a denominator of 7:
\[ b = -\frac{14}{7} + \frac{3}{7} = -\frac{14 - 3}{7} = -\frac{11}{7} \]
Now we have \(m\) and \(b\). The equation of the line in slope-intercept form is:
\[ y = -\frac{1}{7}x - \frac{11}{7} \]
To rewrite this without the fraction in front of \(x\), we can multiply through by \(7\):
\[ 7y = -x - 11 \]
Thus, the slope-intercept form remains:
\[ y = -\frac{1}{7}x - \frac{11}{7} \]
However, since you were looking for it in the form of \(y = -x - \) something, it seems to be:
\[ y = -\frac{1}{7}x - \frac{11}{7} \]
So, according to your question, you can replace the "something" with \(-\frac{11}{7}\):
The equation in slope-intercept form is \(y = -\frac{1}{7}x - \frac{11}{7}\).