Part 1. this is the graph of y=1/2x+10. use the graph to show that equal intervals of x-values have equal differences of y-values. part a of part 1. table # 1 y=-1/2(6)+10= table #2 y=-1/2(10)+10= difference =__ difference =__ part b of part 1 difference in x-values for each interval is difference =(p+k)= part c of part 1 the difference in the y-values for each interval is part d of part 1 does your answer in part c depend on p? if not what does it depend on?

A. y = 7 and y = 5, Difference is 4 and -2 respectively

B. Difference is 4 and (p+k)-p = k

C. Difference is -2

D. Answer in part C does not depend on 'p' but it depends on 'k'.

Step-by-step explanation:

We have .

Part A. Now, the values of y are:

Table 1: i.e. i.e. y = 7

Table 2: i.e. i.e. y = 5

Thus, in Table 2, the difference in x-axis = 14-10 = 4 and the difference in y-axis = 3-5 = -2.

Part B. The difference in x-values for each interval is 4.

The value is constant because = (p+k)-p = p+k-p = k.

Part C. The difference in x-values for each interval is -2.

Part D. As, the difference for y-values is .

So, we get that the answer in part C does not depend on 'p' but it depends on the value of 'k'.

c. prove the lengths are the same.

step-by-step explanation:

you need to prove the segments are congruent. congruent segments have the same length. find the lengths of the segments using the distance formula, and compare them.

answer: c. prove the lengths are the same.

step-by-step explanation:

we are given a graph for system of inequalities.

in order to write the system of inequalities for the given graph, we need to find the inequality for each of the line separately.

let us find the slope of dotted line first.

taking two coordinates on the graph.

let us say (0,0) and (3,1).

let us find the slope of the line now.

slope of the dotted line would be =.

y-intercept of dotted line is y=0 only.

plugging slope m= and b=0 in slope-intercept form y=mx+b, we get

.

the line is shaded up of that dotted line.

therefore, for shading up we would take greater than inequality symbol > .

and because it's a dotted line we would take only > symbol in place of = sign in above equation of line.

therefore, inequality for dotted line would be

let us take two points (3,1) and (0,4) on the solid line.

slope of the solid line would be =.

for the solid line we have y-intercept b= 4.

plugging slope m= -1 and b=4 in slope-intercept form y=mx+b, we get

y = -1x + 4.

the line is shaded down of that solid line.

therefore, for shading down we would take less than inequality symbol < .

and because it's a solid line we would take ≤ symbol in place of = sign in above equation of line.

therefore, inequality for solid line would be