Look at the image above: Could someone please do this for me
2 answers:
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The first line through points (-3, 0) and (-4, -1) is the orange line.
The second line, through (1, 1) and (2, -1) is the purple line.
Since they are both shaded below, the intersection of the shaded regions, is the region colored in blue.
Both lines are included, since they are solid lines.
The equation of the first line can be found as follows:
the slope is
, thus, the equation is:
The equation of the second line can be found as follows:
the slope is
,
thus the equation of the second line is :
We have to decide on the direction of the inequality sign, so we pick a point, for example (0, 4) which is not in the colored regions of the lines,
so we write the inequalities so that they do not hold for (0, 4)
line 1:
y≥x+4
4≥0+4=4 is true, so we change the sign and write : y≤x+4
similarly, line 2:
y≤-2x+3
4≤-2*0+3=3, which is not true, so we have the correct direction.
Note that since the lines were solid, we include the equality case:
Answer:
the shaded region is the solution to the system of inequalities:
i) y≤x+4
ii) y≤-2x+3
The second line, through (1, 1) and (2, -1) is the purple line.
Since they are both shaded below, the intersection of the shaded regions, is the region colored in blue.
Both lines are included, since they are solid lines.
The equation of the first line can be found as follows:
the slope is
The equation of the second line can be found as follows:
the slope is
thus the equation of the second line is :
We have to decide on the direction of the inequality sign, so we pick a point, for example (0, 4) which is not in the colored regions of the lines,
so we write the inequalities so that they do not hold for (0, 4)
line 1:
y≥x+4
4≥0+4=4 is true, so we change the sign and write : y≤x+4
similarly, line 2:
y≤-2x+3
4≤-2*0+3=3, which is not true, so we have the correct direction.
Note that since the lines were solid, we include the equality case:
Answer:
the shaded region is the solution to the system of inequalities:
i) y≤x+4
ii) y≤-2x+3
First, let's find the slope of the line using the slope formula, which is:
((,
) and (
,
) are points on the line)
In context of this problem, we can use the formula to find the slope of the line between the two points:
Now, we can use the slope in the point-slope formula, which will help us find the final equation of the line. (For reference, the point-slope formula is where (
,
) is a point on the line)
In the context of the problem, we could use the formula to find the equation of the line:
The equation of the line is y = -x + 5.