I need serious help, this is hard

Explanation:

M is the midpoint of segment PQ. This means PQ is cut in half into two equal smaller pieces PM and MQ. We can say that PM = MQ.

Furthermore, we can say that PQ is twice as long as either piece, so

We'll use the second equation to say the following:

PQ = 2*MQ

6x+56 = 2*MQ replace PQ with 6x+56

6x+56 = 2*(5x+8) replace MQ with 5x+8

6x+56 = 2*5x + 2*8 distribute

6x+56 = 10x+16

6x+56-10x = 16 subtract 10x from both sides

-4x+56 = 16

-4x = 16-56 subtract 56 from both sides

-4x = -40

x = -40/(-4) divide both sides by -4

x = 10

Once we know the value of x, we use it to find the length of PM

PM = MQ

PM = 5x+8

PM = 5*10+8

PM = 50+8

PM = 58

Note how PQ = 6x+56 = 6*10+56 = 116 is exactly twice as large compared to 58. In other words, 2*58 = 116. This confirms that PQ is twice as long compared to PM or MQ. This helps confirm we have the right answer.

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)