Question

As a computer technician, Andre makes $20 per hour to diagnose a problem and $25 per hour to fix a problem. He works fewer than 10 hours per week, but wants to make at least $200 per week. The inequalities 20x + 25y ≥ 200 and x + y < 10 represent the situation. Which is true of the graph of the solution set? Check all that apply. The line 20x + 25y ≥ 200 has a positive slope and a negative y-intercept. The line x + y < 10 has a negative slope and a positive y-intercept. The line representing 20x + 25y ≥ 200 is solid and the graph is shaded above the line. The line representing x + y < 10 is dashed and the graph is shaded above the line. The overlapping region contains the point (4, 5).

Answer 1

e d g e n u i t y   says the answers are b c and e

Answer 2

For
ax+by=c
the slope is -a/b
20x+25y≥200
slope=-20/25=-4/5
negative slope

yint is where x=0
20(0)+25y≥200
25y≥200
y≥98
positive yint

x+y<10
slope=-1/1=-1
yint is where x=0
y<10
yint is at y=10

since it is equal, it is solid line
to tell if it is above then sub (0,0) and see if true
0≥200
false
shade on side that doesn't have (0,0), shade above line


x+y<10 doesn't have equal under so it is dashed
test (0,0)
0<10
true, it is shaded below

test point (4,5)

20(4)+25(5)≥200
80+125≥200
225≥200
true

4+5<10
9<10
true


so the ones that are true are

The line x + y < 10 has a negative slope and a positive y-intercept.
The line representing 20x + 25y ≥ 200 is solid and the graph is shaded above the line.
The overlapping region contains the point (4, 5).