Answer:
Line: Solid
Shade: Above
m = -4/5
b = 2
(0,2) - True -Yes
(3,4) - True - Yes
(-2,-2) - False - No
Explanation:
Given:
4x + 5y ≥ 10
Questions:
Line: Solid or Dashed?
Shade: Above or Below?
m= [?]
b= [?]
Are these points solution:
Solve:
Inequalities that use '< or >' symbols are plotted with a dashed line. Due to that dashed line means the solution doesn't include the line itself.
< = Less than
> = Greater than
Inequalities that use '≤ or ≥' symbols are plotted with a solid line. Due to that solid line means the solution does includes the line itself
≤ = Less than or equal to
≥ = Greater than or equal to
Therefore, based on the given, the line is solid. Which also means the solution does includes the line itself.
We also know that the given info with the inequalities of "≥".
"≥" Means greater than or equal to which means shade above. If it was "≤ " which means less than or equal to you have to shade below.
To find the m and b we first have to know that;
y = mx + b
m = Slope
b = y-intercept
To find the Slope(m) and b(y-intercept) we first have to put 4x + 5y ≥ 10 in slope-intercept form.
4x + 5y ≥ 10
4x-4x + 5y ≥ 10-4x {Subtract 4x from both sides}
5y ≥ -4x + 10
5y ≥ -4x + 10 {Divided all by 5}
5y/5 ≥ -4x/5 + 10/5
y =-4/5x+2
Hence, now we know that;
m = -4/5
b = 2
To see if the following points {(0,2) (3,4) (-2,-2)} are solutions for 4x + 5y ≥ 10
All we have to do is to substitute it in.
Starting with (0,2)
x = 0
y = 2
4(0) + 5(2) ≥ 10
0 + 10 ≥ 10
10≥ 10
True. 10 isn't greater than 10 but- It's equal to 10. ≥ Means greater than or equal to Hence, (0,2) is a solution.
Next we have (3,4)
x = 3
y = 4
4(3) + 5(4) ≥ 10
12 + 20 ≥ 10
32 ≥ 10
True. 32 is greater than 10 - Hence, (3,4) is a solution.
Finally we have (-2,-2)
x = -2
y = -2
4(-2) + 5(-2) ≥ 10
-8 + -10 ≥ 10
-18 ≥ 10
False. Although you may probably think 18 is greater than 10 it is not correct. -18 isn't greater than 10 due to that it is negative.
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