Question

the equation of the line passing through the points A and B. A(5,1/2), B(-1,3/4)

Answer 1

The equation of the line passing through the points A and B. $A(5,1/2), B(-1,3/4)$.

**Solution:**

First find the slope

$$k = \frac{y_2 - y_1}{x_2 - x_1}$$ $$k = \frac{\frac{3}{4} - \frac{1}{2}}{-1 - 5} = \frac{\frac{3 - 2}{4}}{-6} = \frac{\frac{1}{4}}{-6} = -\frac{1}{24}$$

So slope of the line is equal $-\frac{1}{24}$

Then use $y = kx + b$, and substitute one set of points into the equation:

$$\frac{1}{2} = -\frac{1}{24} * 5 + b$$ $$b = \frac{1}{2} + \frac{5}{24} = \frac{17}{24}$$

The equation is $y = -\frac{1}{24} x + \frac{17}{24}$

**Answer:** $y = -\frac{1}{24} x + \frac{17}{24}$