Write an equation in slope-intercept form for the line that satisfies the following condition.

passes through (5, 14), parallel to the line that passes through (12, 2) and (35, 19)

the line through (12, 2) and (35, 19) has slope (19-2)/(35-12) = 17/23

the line through (5,14) with that slope is

(y-14)/(x-5) = 17/23
23(y-14) = 17(x-5)
23y-322 = 17x - 85
y = 17/23 x + 237/23

To find the equation of a line parallel to another line, we first need to find the slope of the given line. The slope of a line can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

Given the points (12, 2) and (35, 19), we can calculate the slope of the given line:

slope = (19 - 2) / (35 - 12) = 17 / 23

Since the line we want to find is parallel to this line, it will have the same slope. Now, we can use the slope-intercept form of a line, which is:

y = mx + b

where "m" is the slope and "b" is the y-intercept.

Since the line passes through (5, 14), we can substitute these values into the equation to solve for the y-intercept:

14 = (17 / 23) * 5 + b
14 = (85 / 23) + b

To find the y-intercept b, we can rearrange the equation:

b = 14 - (85 / 23)
b = (322 - 85) / 23
b = 237 / 23

Now we have the slope (17/23) and the y-intercept (237/23), so we can rewrite the equation of the line in slope-intercept form:

y = (17/23) * x + 237/23

Therefore, the equation of the line that satisfies the given condition is:

y = (17/23) * x + 237/23