Reducing a nonlinear relation to straight-line form · Short practice

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Recall

Straight-line transformations of data — objective 1

Maths4U Original · Short practice

A positive model y=Axⁿ is plotted with \(\displaystyle U=\log _{2}x\) and \(\displaystyle V=\log _{2}y\). The line passes through \(\left( 1, \ 6\right)\) and \(\left( 3, \ 12\right)\).

Find the intercept of the transformed line.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Straight-line transformations of data — objective 1

Maths4U Original · Short practice

A positive model y=Axⁿ is plotted with \(\displaystyle U=\log _{2}x\) and \(\displaystyle V=\log _{2}y\). The line passes through \(\left( 1, \ 8\right)\) and \(\left( 3, \ 16\right)\).

Find the intercept of the transformed line.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Method

Straight-line transformations of data — objective 2

Maths4U Original · Short practice

A positive model y=Axⁿ is plotted with \(\displaystyle U=\log _{2}x\) and \(\displaystyle V=\log _{2}y\). The line passes through \(\left( 1, \ 8\right)\) and \(\left( 3, \ 16\right)\).

Find its gradient.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Straight-line transformations of data — objective 2

Maths4U Original · Short practice

A positive model y=Axⁿ is plotted with \(\displaystyle U=\log _{2}x\) and \(\displaystyle V=\log _{2}y\). The line passes through \(\left( 1, \ 10\right)\) and \(\left( 3, \ 20\right)\).

Find its gradient.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Apply

Straight-line transformations of data — objective 3

Maths4U Original · Short practice

A positive model y=Axⁿ is plotted with \(\displaystyle U=\log _{2}x\) and \(\displaystyle V=\log _{2}y\). The line passes through \(\left( 1, \ 10\right)\) and \(\left( 3, \ 20\right)\).

Find A.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Straight-line transformations of data — objective 3

Maths4U Original · Short practice

A positive model y=Axⁿ is plotted with \(\displaystyle U=\log _{2}x\) and \(\displaystyle V=\log _{2}y\). The line passes through \(\left( 1, \ 3\right)\) and \(\left( 3, \ 7\right)\).

Find A.

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Check understanding

Straight-line transformations of data — objective 4

Maths4U Original · Short practice

A positive model y=Axⁿ is plotted with \(\displaystyle U=\log _{2}x\) and \(\displaystyle V=\log _{2}y\). The line passes through \(\left( 1, \ 3\right)\) and \(\left( 3, \ 7\right)\).

Find the model output y at \(\displaystyle x=2\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

Fresh review variant

Straight-line transformations of data — objective 4

Maths4U Original · Short practice

A positive model y=Axⁿ is plotted with \(\displaystyle U=\log _{2}x\) and \(\displaystyle V=\log _{2}y\). The line passes through \(\left( 1, \ 5\right)\) and \(\left( 3, \ 11\right)\).

Find the model output y at \(\displaystyle x=2\).

Enter one exact number or fraction. These checks support non-calculator practice. Give full reasoning separately for written problems.

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