Answer:
y = -2x + 4.
Step-by-step explanation:
Use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
Here the slope m = -2, x1 = 3 and y1 = -2 so:
y - (-2) = -2(x - 3)
y + 2 = -2x + 6
y = -2x + 4 (answer).
"(-1, 0)" is the one ordered pair among the following choices given in the question that <span>is not a solution to the inequality y -3x - 2. The correct option among all the options that are given in the question is option "C".
"</span>(0, 4)" is the one ordered pair among the following choices given in the question that is a solution to the inequality y -3x - 2. The correct option among all the options that are given in the question is option "B".
Problem 5
<h3>Answers:</h3>
- Domain = which in interval notation is [-3, 3]
- Range = which is also [-3, 3] in interval notation
- Is it a function? Yes
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Explanation:
The domain is the set of allowed x values. Here we see that x = -3 is the smallest possible x value and x = 3 is the largest. So x is anything between -3 and 3, including both endpoints. We write to indicate this. That converts to [-3,3] in interval notation. The square brackets mean "include this endpoint".
The range is the same story, but with the y values. Coincidentally, the range has the same exact endpoints as the domain does. This won't always be the case.
This graph is a function because it is not possible to draw a single vertical line through more than one point on the relation curve. Any x value pairs with one and only one y value. The next problem is a different story.
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Problem 6
<h3>Answers:</h3>
- Domain = which in interval notation is [-4, 4]
- Range = and that is [-3,3] in interval notation
- Is it a function? No
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Explanation:
We use the same idea as before. The left most point tells us the smallest x value, and the right most point tells us the largest x value. The domain is everything in this interval including both endpoints. The range is a similar story but we're looking for the lowest and highest points to get the smallest and largest y values respectively.
This relation is not a function because this graph fails the vertical line test. It is possible to pass a single straight vertical line through more than one point on this curve. For example, draw a vertical line through x = 2 and it crosses the circle twice. This means the input x = 2 leads to more than one output, but a function must have exactly one output for any valid domain input value.
Substitute any number in for x and solve for y. Say that x=1.
y=5(1)-7
y=5-7
y=-2
The ordered pair would be (1,-2).