What is the equation of the line that is parallel to the line 5x + 2y = 12 and passes through the point (−2, 4)? y = – x – 1y =
2 answers:
Answer: The required equation of the line is
Step-by-step explanation: We are given to find the equation of the line that is parallel to the following line and passes through the point (-2, 4) :
We know that
the slope-intercept form of the equation of a straight line is given by
where m is the slope of the line.
From equation (i), we have
So, the slope of line (i) is given by
We know that the slopes of two parallel lines are equal. So, the slope of the new line will be
Since the line passes through the point (-2, 4), so its equation will be
Thus, the required equation of the line is
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<u>Solution-</u>
The given inequalities are,
<u>Part A</u>
As the former inequality is only '<' so it will be represented as dotted line, but in case of the later inequality there is '≥' so it will be represented as a solid line.
This happens because in only '<, >' the values must be either lesser or greater than y, they can't take the values of y, but in case of '≤, ≥' the values can be equal to y.
Taking origin (0, 0) and putting in the first inequality.
As the equation does not satisfy, so the shaded area will be on the other side of the origin.
Again taking origin (0, 0) and putting in the second inequality.
As the equation does not satisfy, so the shaded area will be on the other side of the origin.
The second attachment contains the feasible region.
<u>Part B</u>
In order to know whether the point (3, −7) is included in the solution area for the system or not, we must put it in both the equations, if it satisfies both then only it is within the solution area.
As the point (3, -7) only satisfies first inequality, but not the second inequality so this point won't be in the solution area.
