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Sagot :
Great question! To determine the linear inequality represented by the graph, let's analyze the given information.
We are told that the dashed straight line has a positive slope and goes through the points (-3, -7) and (0, 2).
To find the slope of the line, we can use the formula:
slope = (change in y) / (change in x)
Using the given points, we can calculate the slope:
slope = (2 - (-7)) / (0 - (-3))
= 9 / 3
= 3
Since the slope is positive, we can conclude that the line is ascending from left to right.
Now, let's look at the y-intercept. From the equation of a line (y = mx + b), the y-intercept is the value of y when x is 0. In this case, the y-intercept is 2.
Putting it all together, the equation of the line is y = 3x + 2.
Now, let's determine the shading. We are told that everything to the left of the line is shaded. Since the line has a positive slope, the shaded region should be below the line.
Therefore, the correct linear inequality represented by the graph is y < 3x + 2.
Does that make sense? Do you have any further questions?
We are told that the dashed straight line has a positive slope and goes through the points (-3, -7) and (0, 2).
To find the slope of the line, we can use the formula:
slope = (change in y) / (change in x)
Using the given points, we can calculate the slope:
slope = (2 - (-7)) / (0 - (-3))
= 9 / 3
= 3
Since the slope is positive, we can conclude that the line is ascending from left to right.
Now, let's look at the y-intercept. From the equation of a line (y = mx + b), the y-intercept is the value of y when x is 0. In this case, the y-intercept is 2.
Putting it all together, the equation of the line is y = 3x + 2.
Now, let's determine the shading. We are told that everything to the left of the line is shaded. Since the line has a positive slope, the shaded region should be below the line.
Therefore, the correct linear inequality represented by the graph is y < 3x + 2.
Does that make sense? Do you have any further questions?
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