write an equation of the line ik slope-intercept form y = mx + b containing the points (1,6) and (5,5)

Solution:
1. Given points:
* (1, 6)
* (5, 5)

2. Calculate the slope m using the slope formula:
m = \frac{y_2 - y_1}{x_2 - x_1}
m = \frac{5 - 6}{5 - 1}
m = \frac{-1}{4}
m = -\frac{1}{4}

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

4. Substitute one of the points (1, 6) and the slope m = -\frac{1}{4} into the equation:
y - 6 = -\frac{1}{4}(x - 1)

5. Simplify to get the equation in slope-intercept form y = mx + b:
y - 6 = -\frac{1}{4}x + \frac{1}{4}
y = -\frac{1}{4}x + \frac{1}{4} + 6
y = -\frac{1}{4}x + \frac{1}{4} + \frac{24}{4}
y = -\frac{1}{4}x + \frac{25}{4}

6. The equation of the line in slope-intercept form is:
y = -\frac{1}{4}x + \frac{25}{4}