Find the equation for the line L graphed in red in the figur

Find the equation for the line L (graphed in red) in the figure below. Note the x-coordinate of the point Q is 4, y-coordinate of the point P is 29, and the parabola (graphed in blue) has equation y = x^2 + 4.

T-Mobile 12:07 AM e webwork.colorado.edu Prev Up Next (1 pt) Find the equation for the line L (graphed in red) in the figure below. Note the T-coordinate of the point Q is 4, y-coordinate of the point P is 29, and the parabola (graphed in blue) has equation y = x2 + 4. 29 click on the image to enlarge) Preview Answers Submit Answers You have attempted this problem 2 times.

Solution

Line L crosses the parabola y =x^2 +4 two times

P ---( x, 29) and Q --->( 4, y)

Lets find P and Q by plugging the parabola equation:

P ( x, 29) : 29 = x^2 +4---> x = +/- 5

we would take x = -5 as P is in IInd quadrant

P ---( -5 , 29)

Now find Q ( 4, y) : y = 4^2 +4 = 20

Q = ( 4, 20)

Now find slope of equation L from P and Q : m =( 20 -29)/( 4- -5) = - 9/9 = -1

Std equation of line y = mx +c ; c is the y intercept:

20 = -1*4 +c ---> c = 24

So, Line L : y = -x +24