Mandy used the input and output in this table to write ratios. She concluded that because that they are not all equivalent, this
is not a proportional relation ship. Is she correct. Explain.I dont get what she means by, "because they are not all equivalent"
1 answer:
The problem is stating that Mandy found the ratio between input and output of many points on the graph, which are displayed by the fractions. Mandy's conclusion was that they were not equivalent, meaning they were different and that is why the function is not proportional. Mandy's conclusion is wrong, the relation is proportional. If we take all the functions we have:
Where the input is the denominator and the output is the numerator we will have a ratio of "5". Mandy's mistake was to invert the last fraction, she inserted the output in the denominator, this is why she said the were different.
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First let's try to find the equation in this form : <span>y = mx + c
The gradient is given 3 . In a line's equation, x's coefficient represents the line's gradient.
So equation of a line with the gradient of 3, would look like this ;
</span>
<span>
Now a point that the line passes through is given, (1, 2)
This point's x-coordinate is 1 and y-coordinate is 2.
So we'll plug its x-coordinate value in the equation and also y-coordinate value. So we can solve it.
As you know, </span>
and 
We found c = -1
Also in a line's equation, c is constant and it represents the line's y-intercept
So let's build the line's equation.
and 
We found the line's equation in this form,
Now let's turn it into this form,
Final answers,
and
I hope this was clear enough :)
<span>
</span>
The gradient is given 3 . In a line's equation, x's coefficient represents the line's gradient.
So equation of a line with the gradient of 3, would look like this ;
</span>
<span>
Now a point that the line passes through is given, (1, 2)
This point's x-coordinate is 1 and y-coordinate is 2.
So we'll plug its x-coordinate value in the equation and also y-coordinate value. So we can solve it.
As you know, </span>
We found c = -1
Also in a line's equation, c is constant and it represents the line's y-intercept
So let's build the line's equation.
We found the line's equation in this form,
Now let's turn it into this form,
Final answers,
and
I hope this was clear enough :)
<span>
</span>