Question

A bridge being designed will cross the river at a right angle. The equation of the left bank of the river is

y=2x+8. The center of the bridge will pass through (0, 2). What is the equation of the line representing the bridge?

Answer 1

The equation of the bridge, which crosses the river at a right angle to the river bank with an equation of y=2x+8 and passes through the center point (0, 2), is y = -1/2x + 2. This is derived using the negative reciprocal of the slope of the river bank's line.

Step-by-step explanation:

The equation of the left bank of the river is y = 2x + 8. The slope of this line is 2, which means for every increase in x by 1, y increases by 2. This slope represents the 'rise over run'.

Since the bridge is to cross the river at a right angle, the slope of the bridge must be the negative reciprocal of the slope of the river bank. Therefore, the slope of the bridge will be -1/2.

Given that the center of the bridge passes through the point (0, 2), we can use the point-slope form to derive the equation of the bridge. Knowing that the y-intercept (b) is 2 because when x is 0, y is 2, the equation of the bridge is:

y = -1/2x + 2.