write the equation of the line passing through each of the given points with the indicated slope. give your results in slope-intercept form. (0, 5) , m = 1/4

To find the equation of the line passing through the given points (0, 5) with a slope of 1/4, we can use the slope-intercept form of a linear equation.

The slope-intercept form is given by:
y = mx + b

Where:
- m is the slope of the line, and
- b is the y-intercept (the point where the line crosses the y-axis).

We are given the slope (m = 1/4), and one of the points through which the line passes (0, 5). Let's substitute these values into the slope-intercept form to find the equation.

Substituting m = 1/4, x = 0, and y = 5:
5 = (1/4)(0) + b

Since (1/4)(0) equals 0, we simplify the equation to:
5 = 0 + b

Therefore, b = 5.

Now, we have the value of the y-intercept (b = 5). We can substitute it back into the slope-intercept form to write the equation of the line:
y = (1/4)x + 5

Hence, the equation of the line passing through the points (0, 5) with a slope of 1/4, in slope-intercept form, is y = (1/4)x + 5.