To find the equation of the line in slope-intercept form \(y = mx + b\), we first need to determine the slope \(m\) using the given points from the table:
The points are:
- \( (1, -5) \)
- \( (2, 0) \)
- \( (3, 5) \)
The slope \(m\) can be calculated using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
We can choose any two points. Let's take points \((1, -5)\) and \((2, 0)\):
\[ m = \frac{0 - (-5)}{2 - 1} = \frac{5}{1} = 5 \]
Now that we have the slope \(m = 5\), we can use one of the points to find the y-intercept \(b\).
Let's use the point \((2, 0)\):
Substituting \(x = 2\) and \(y = 0\) into the slope-intercept form:
\[ 0 = 5(2) + b \] \[ 0 = 10 + b \] \[ b = -10 \]
Thus, the equation of the line in slope-intercept form is:
\[ y = 5x - 10 \]