To find the equation of the line in slope-intercept form (\(y = mx + b\)), we need to calculate the slope (\(m\)) using the given points and then find the y-intercept (\(b\)).
Given the points:
- \((-3, 0)\)
- \((-2, 3)\)
- \((-1, 6)\)
We can calculate the slope (\(m\)) using two points, for example, \((-3, 0)\) and \((-2, 3)\).
The formula for slope is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using \((-3, 0)\) as \((x_1, y_1)\) and \((-2, 3)\) as \((x_2, y_2)\): \[ m = \frac{3 - 0}{-2 - (-3)} = \frac{3}{1} = 3 \]
Now, we have the slope \(m = 3\).
Next, we need to find the y-intercept (\(b\)). We can use one of the points; let's use the point \((-2, 3)\) and the slope we found.
Substituting \(x\) and \(y\) into the slope-intercept equation: \[ y = mx + b \implies 3 = 3(-2) + b \] \[ 3 = -6 + b \] \[ b = 3 + 6 = 9 \]
Now we have both the slope and the y-intercept:
- Slope \(m = 3\)
- Y-intercept \(b = 9\)
The equation of the line in slope-intercept form is: \[ y = 3x + 9 \]