Answer:
Line: Dashed
Shade: Below
m = -3/4
b = 3
(0,3) - False - No
(2,4) - True - Yes
(-1,-2) - False - No
Explanation:
Given:
-3x < 4y - 12
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 Dashed. Which also means the solution doesn't includes the line itself.
We also know that the given info with the inequalities of "<".
"<" Means Less than which means shade below. If it was "> " which means greater than you have to shade above.
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 -3x < 4y - 12 in slope-intercept form.
-3x < 4y - 12
y > -3/4x + 3
Hence,
m = -3/4
b = 3
To see if the following points {(0,3) (2,4) (-1,-2)} are solutions for -3x <4y-12
All we have to do is to substitute it in.
Starting with (0,3)
x = 0
y = 3
-3(0) < 4(3) - 12
0 < 0
False. 0 isn't less than 0- it equal to 0. Hence it isn't a solution to -3x < 4y - 12
Next (2,4)
x = 2
y = 4
-3(2) < 4(4) -12
-6 < 4
True. -6 is less than 4. Hence it is a solution to -3x < 4y - 12
Finally, we have (-1,-2)
x = -1
y = -2
-3(-1) < 4(-2) -12
3 < -20
False. 3 isn't less than -20. Hence it isn't a solution to -3x < 4y -12
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