Answer:
- vertex (3, -1)
- y-intercept: (0, 8)
- x-intercepts: (2, 0), (4, 0)
Step-by-step explanation:
You are being asked to read the coordinates of several points from the graph. Each set of coordinates is an (x, y) pair, where the first coordinate is the horizontal distance to the right of the y-axis, and the second coordinate is the vertical distance above the x-axis. The distances are measured according to the scales marked on the x- and y-axes.
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<h3>Vertex</h3>
The vertex is the low point of the graph. The graph is horizontally symmetrical about this point. On this graph, the vertex is (3, -1).
<h3>Y-intercept</h3>
The y-intercept is the point where the graph crosses the y-axis. On this graph, the y-intercept is (0, 8).
<h3>X-intercepts</h3>
The x-intercepts are the points where the graph crosses the x-axis. You will notice they are symmetrically located about the vertex. On this graph, the x-intercepts are (2, 0) and (4, 0).
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<em>Additional comment</em>
The reminder that these are "points" is to ensure that you write both coordinates as an ordered pair. We know the x-intercepts have a y-value of zero, for example, so there is a tendency to identify them simply as x=2 and x=4. This problem statement is telling you to write them as ordered pairs.
8, 8 2/7, 26/3, 8.8
(You have to change 8 2/7 to 8.28 and 26/3 to 8.66
Answer:
Step-by-step explanation:
1. Swap sides
Swap sides:
2. Isolate the y
Multiply to both sides by 18:
Group like terms:
Simplify the fraction:
Multiply the fractions:
Simplify the arithmetic:
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Why learn this:
- Linear equations cannot tell you the future, but they can give you a good idea of what to expect so you can plan ahead. How long will it take you to fill your swimming pool? How much money will you earn during summer break? What are the quantities you need for your favorite recipe to make enough for all your friends?
- Linear equations explain some of the relationships between what we know and what we want to know and can help us solve a wide range of problems we might encounter in our everyday lives.
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Terms and topics
- Linear equations with one unknown
The main application of linear equations is solving problems in which an unknown variable, usually (but not always) x, is dependent on a known constant.
We solve linear equations by isolating the unknown variable on one side of the equation and simplifying the rest of the equation. When simplifying, anything that is done to one side of the equation must also be done to the other.
An equation of:
in which 
and 
are the constants and 
is the unknown variable, is a typical linear equation with one unknown. To solve for in this example, we would first isolate it by subtracting from both sides of the equation. We would then divide both sides of the equation by resulting in an answer of:
