Consider the system of equations shown below. y = negative 5 x + 1. y = negative 5 x + 10 When graphed, the system consists of two lines that will never meet, no matter how far they are extended. Why are the lines parallel? The linear equations have the same slope and y-intercept. The linear equations have different slopes and y-intercepts. The linear equations have the same slope but different y-intercepts. The linear equations have different slopes but the same y-intercept.

The reason why both graphs are parallel because they have the same slope but different y-intercept.

Think about it. If both graphs have same slope and same y-intercept. The graph will intercept each others infinitely.

Then if we change the y-intercept into any numbers that aren't the same as another equations for ex.

y = -5x+1 and y = -5x+10

then we will get the parallel graph. Or if you solve the equation, the equation will not be true, thus giving the graph parallel.

But if it is y = -5x+1 and y = -5x+1 which both are the same graph. Then the graph will intercept each others infinitely. Or if we solve the equation, we will get 0 = 0 which makes the equation true for all real numbers.

Therefore, the reason why both graphs are parallel is because that they have the same slope but different y-intercept.

That's all.

55.44 inches

step-by-step explanation:

part a. assuming a perfectly linear relationship, we can find the slope from the first two data points.

slope = m = (change in rainfall)/(change in years)

= (61.80 -62.33)/(2005 -2004) = -0.53/1 = -0.53

then the point-slope form of the equation of the line can be written as

y = m(x -h) +k . . . . . m = -0.53, (h, k) = (0, 62.33)

y = -0.53x +62.33 . . . x = years after 2004

part b. in 2017, x = 2017 -2004 = 13. then the predicted rainfall is

y = -0.53·13 +62.33 = 55.44 . . inches

the predicted rainfall in 2017 is 55.44 in.