Which shows the graph of the solution set of 2x+3y≤6?
2 answers:
Answer:
Option (a) is correct.
Step-by-step explanation:
Given : equation 2x + 3y ≤ 6
We have to choose out of given option the graph that shows the graph of the solution set of 2x + 3y ≤ 6
Consider the given equation 2x + 3y ≤ 6
We first find the points where the equation cut x- axis and y-axis.
Thus,
For x - axis put y = 0 ,
We get 2x + 3(0) ≤ 6 ⇒ 2x ≤ 6 ⇒ x ≤ 3
Thus, point (3,0)
For y - axis put x = 0 ,
We get 2(0) + 3y ≤ 6 ⇒ 3y ≤ 6 ⇒ y ≤ 2
Thus, point (0,2)
For region we choose a test point and find the value of x and y on that test point and check whether it satisfy the inequality satisfies or not.
Consider the point (0, 0) , then inequality becomes,
2(0) + 3(0) ≤ 6 ⇒ 0 ≤ 6 (true)
Hence, region below the line will be considered.
Thus, Option (a) is correct.
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Answer:
Options (A) and (C)
Step-by-step explanation:
From table attached,
Let the equation of a linear equation that represents the input-output values in the table is,
y - y' = m(x - x')
Where (x', y') is a point lying on the graph.
And m = slope of the line passing through two points and
m =
Slope of the line passing through (0, 11) and (1, 5) will be,
m =
m = -6
Therefore, equation of the line passing through (0, 11) and slope = -6 will be,
y - 11 = -6(x - 0)
Equation of a line passing through (1, 5) and slope = -6 will be,
y - 5 = -6(x - 1)
Equation of a line passing through (2, -1) and slope = -6 will be,
y + 1 = -6(x - 2)
Equation of a line passing through (3, -7) and slope = -6 will be,
y + 7 = -6(x - 3)
Therefore, Options (A) and (C) are the correct options.