What is the equation of the line? P(-4;2) Q(2;0)

Solution:
1. Given points:
* P(-4, 2)
* Q(2, 0)

2. Find the slope m of the line using the formula:
m = \frac{y_2 - y_1}{x_2 - x_1}

3. Substituting the coordinates of the points into the formula:
* y_1 = 2, y_2 = 0, x_1 = -4, x_2 = 2

4. Calculate the slope:
m = \frac{0 - 2}{2 - (-4)} = \frac{-2}{2 + 4} = \frac{-2}{6} = -\frac{1}{3}

5. Use the point-slope form of a line equation:
y - y_1 = m(x - x_1)

6. Substituting one of the points and the slope into the equation:
* Point P(-4, 2):
y - 2 = -\frac{1}{3}(x - (-4))

7. Simplify the equation:
y - 2 = -\frac{1}{3}(x + 4)
y - 2 = -\frac{1}{3}x - \frac{4}{3}

8. Add 2 to both sides:
y = -\frac{1}{3}x - \frac{4}{3} + \frac{6}{3}
y = -\frac{1}{3}x + \frac{2}{3}

9. The equation of the line in slope-intercept form is:
y = -\frac{1}{3}x + \frac{2}{3}