To find the slope \( m \) of the line that goes through the points given in the table, we can use any two points from the dataset. Let's take the first two points:
- Point 1: \((-12, 1)\)
- Point 2: \((-9, -3)\)
The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Substituting the coordinates of our points:
\[ m = \frac{-3 - 1}{-9 - (-12)} = \frac{-4}{-9 + 12} = \frac{-4}{3} \]
Thus, the slope \( m \) is \(-\frac{4}{3}\).
Next, we need to find the equation of the line in slope-intercept form, which is given by:
\[ y = mx + b \]
Where \( m \) is the slope and \( b \) is the y-intercept. We already found that \( m = -\frac{4}{3} \). To find \( b \), we can use one of the points. Let's use the point \((-12, 1)\):
\[ 1 = -\frac{4}{3}(-12) + b \]
Calculating the right side:
\[ 1 = \frac{48}{3} + b \] \[ 1 = 16 + b \]
Now, we solve for \( b \):
\[ b = 1 - 16 = -15 \]
So, the y-intercept \( b \) is \(-15\).
Now we can write the equation of the line in slope-intercept form:
\[ y = -\frac{4}{3}x - 15 \]
In summary:
- The slope of the line is \(-\frac{4}{3}\).
- The equation of the line in slope-intercept form is \( y = -\frac{4}{3}x - 15 \).