Vicky records the low temperature for three consecutive days. between the first and second days the temperature increased 6 degrees. between the second and third days the temperature decreased 3 degrees. on the third day the low temperature was –6º. what was the low temperature on the first day? –15 degrees –9 degrees –3 degrees 3 degrees

This is the same as y = -0.5x+2

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Explanation:

Refer to the diagram below.

The blue line is the graph of y = 2x+8, which is the left bank of the river.

For now, ignore the y = (-1/2)x+2 in the diagram and pretend we don't know that just yet. The red line is the bridge and it's some linear equation in the form y = mx+b. We're told the bridge is perpendicular to the river, so the bridge must also be perpendicular to the riverbank.

The blue line has slope m = 2. Apply the negative reciprocal to this to end up with -1/2. This is the perpendicular slope, and the slope of the red line. Note how the two slopes (2 and -1/2) multiply to -1. Any two perpendicular lines will have their slopes multiply to -1, as long as neither line is vertical or horizontal.

Since we want the bridge to pass through (0,2), this must mean the y intercept is b = 2.

So with m = -1/2 and b = 2, we go from y = mx+b to y = (-1/2)x + 2 which is the equation of the bridge shown in red.

This is the same as y = -0.5x + 2 since -1/2 = -0.5