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If a ship's path is mapped on a coordinate grid, it follows a straight-line path of slope 4 and passes through point (1, 2).

Part A: Write the equation of the ship’s path in slope-intercept form. (2 points)

Part B: A second ship follows a straight line, with the equation x + 4y − 20 = 0. Are these two ships sailing perpendicular to each other? Justify your answer. (2 points)

 Mar 7, 2018
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Part A:

We want the equation of the line with a slope of  4  that passes through the point  (1, 2)

 

We know a point  (1, 2)  and we know the slope  4

So we can write the equation in point-slope form.

 

y - 2   =   4(x - 1)            To get this into slope-intercept form, distribute the  4 .

y - 2   =   4x - 4              Add  2  to both sides.

y  =  4x - 2

 

Part B:

Is the line   x + 4y - 20  =  0   perpendicular to the line  y  =  4x - 2   ?
 

The slope of the line   y  =  4x - 2   is  4.

 

To find the slope of the line  x + 4y - 20  =  0  , let's get the equation into slope-intercept form.

 

x + 4y - 20  =  0       Add  20  to both sides.

x + 4y  =  20            Subtract  x  from both sides.

4y   =   -x + 20         Divide both sides by  4 .

y   =   -\(\frac14\)x + 5          Now we can see that the slope of this line is  -\(\frac14\) .

 

Since   -\(\frac14\)   is the negative reciprocal of  4  , these lines are perpendicular.

 

Yes, the two ships are sailing perpendicular to each other.

 Mar 7, 2018

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