Complete the statement.
1 answer:
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Answer:
<em>The table shows a proportional relationship: YES</em>
<em>The constant of proportionality is k=7</em>
<em>y = 7x</em>
Step-by-step explanation:
<u>Proportions</u>
A direct proportion is a relation between variables where their ratio is a constant value. This means that if y and x are proportional, then:
y = kx
Where k is the constant of proportionality. It can be calculated by solving the equation for k:
We are given a table with 4 pairs of values. If the relationship between the variables is proportional, then the ratio y/x should be constant.
Let's verify some points:
Since all the ratios are equal,
The table shows a proportional relationship: YES
The constant of proportionality is k=7
The equation for the relationship is
y = 7x
Explanation:
The solution set for a system of equation is the set of points where the graphs of the equations intersect.
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<h3>general case</h3>A system will have <em>one solution</em> if there is a <em>single point of intersection</em> of the graphs of the equations.
A system will have <em>no solutions</em> if the graphs have <em>no points of intersection</em>.
A system will have an <em>infinite</em> number of <em>solutions</em> if the graphs <em>intersect at an infinite number of points</em>.
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<h3>linear equations</h3>When the equations are linear equations, their graphs are straight lines. If the lines have different slopes, they must intersect at exactly one point: there will be one solution.
If the lines have the same slope, there are two possibilities:
- the lines are parallel -- no solutions
- the lines are coincident -- infinite solutions
The attached graph illustrates these cases.
- the red and blue lines are the graphs of a system of equations with one solution. Those lines have different slopes
- the blue and green lines are the graphs of a system of equations with no solution. Those lines are parallel.
- The red and (dotted) purple lines are the graphs of a system of equations with infinite solutions. Those lines are coincident.
