Eisimpleirean

Freagairt

Obraich a-mach caisead na loidhne a tha a' ceangal nam puingean A(5, 8) agus B(3, 10)

\[A({x_1},{y_1})\,agus\,B({x_2},{y_2})\]

\[A(5,8)\,agus\,B(3,10)\]

\[{m_{AB}} = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\]

\[{m_{AB}} = \frac{{10 - 8}}{{3 - 5}}\]

\[{m_{AB}} = \frac{{10 - 8}}{{3 - 5}}\]

\[{m_{AB}} = \frac{2}{{ - 2}} = - 1\]

Feuch a-nis a' cheist gu h-ìosal.

Question

Obraich a-mach caisead na loidhne gu h-ìosal:

Diagram of a line graph

Gus caisead na loidhne seo obrachadh a-mach leis an fhoirmle, tagh an toiseach dà cho-chomharra a tha air an loidhne.

Faodar dà phuing sam bith a thaghadh, ach airson an eisimpleir gu h-ìosal, chaidh na puingean (2,7) agus (9,3) a thaghadh.

Ma thèid puingean eile a thaghadh, bidh am freagairt fhathast an aon rud.

Diagram of a line graph with plotted points (2, 7) and (9, 3)

\[({x_1},{y_1})\,agus\,({x_2},{y_2})\]

\[(2,7)\,agus\,(9,3)\]

\[m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}\]

\[m = \frac{{3 - 7}}{{9 - 2}}\]

\[m = \frac{{ - 4}}{7}\]

Caiseadan loidhnichean sònraichte

Loidhnichean co-shìnte

Tha an aon chaisead aig loidhnichean co-shìnte.

Diagram of parallel lines

Loidhnichean bheartagail

Tha caisead aig loidhnichean co-shìnte a tha neo-chomharraichte; co-aontar \(x = a\)

Diagram of a vertical line

Loidhnichean còmhnard

Tha caisead de neoni aig loidhnichean còmhnard; co-aontar \(y = b\)

Diagram of a horizontal line

Question

Dè na loidhnichean a tha còmhnard agus dè an fheadhainn a tha bheartagail?

\[x=3\]

\[y=-6\]

\[y=5\]

\[x=-2\]

'S e còmhnard \(y=-6\) agus \(y=5\)

'S e bheartagail \(x=3\) agus \(x=-2\)

Question

Obraich a-mach caisead na loidhne a tha a' dol tro na puingean \( (3, 4)\) agus \((7, 12)\).

\((x_{1}, y_{1})\) agus \((x_{2}, y_{2})\)

\( (3, 4)\) agus \((7, 12)\)

\[m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\]

\[=\frac{12-4}{7-3}\]

\[=\frac{8}{4}\]

\[=2\]

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