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All but one of the straight lines above follow the general formula \$y=mx+c\$ where \$m\$ is a constant denoting the gradient of a line and \$c\$ is a constant denting the \$y\$-intercept of a line.

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The gradient (given by \$m\$), indicates the slope of a straight line. Where this is positive, the \$y\$-coordinate along the line increases by \$m\$ for every increase in the value of \$x\$ by \$1\$. For example, \$y=3x\$ indicates that for every increase in the value of \$x\$ by \$1\$, the value of \$y\$ increases by \$3\$. Where there is no \$m\$ (i.e. \$y=c\$), the line is straight and horizontal as the value of \$y\$ has no dependence on the value of \$x\$.

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The \$y\$-intercept (given by \$c\$), indicates the point where the line passes through the \$y\$-axis. If the line equation has no \$c\$ (i.e. \$y=mx\$), the line has a \$y\$ intercept of \$0\$ (passing through the origin).

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We can use our knowledge of the slope of the line and the \$y\$-intercept to then judge which points on the graph correspond to which equations.

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A:

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\$y=\\simplify{{m1}x+{c1}}\$  gives us \$m=\\var{m1}\$ and \$c=\\var{c1}\$.

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B:

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\$y=\\simplify{{m2}x+{c2}}\$  gives us \$m=\\var{m2}\$ and \$c=\\var{c2}\$.

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C:

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\$y=\\simplify{{m3}x+{c3}}\$  gives us \$m=\\var{m3}\$ and \$c=\\var{c3}\$.

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D:

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\$y=\\simplify{{c4}}\$  gives us \$m=0\$ and \$c=\\var{c1}\$.

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E:

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\$x=\\var{c5}\$  is the exception to the \$y=mx+c\$ form of writing straight line equations. This equation gives a value for \$x\$ independent of the value of \$y\$ so a straight, vertical line is formed at the \$x\$-coordinate \$\\var{c5}\$.

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\$A_0\$

", "

\$B_0\$

", "

\$C_0\$

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\$D_0\$

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\$E_0\$

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\$y=\\simplify{{m1}x+{c1}}\$

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\$y=\\simplify{{m2}x+{c2}}\$

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\$y=\\simplify{{m3}x+{c3}}\$

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\$y=\\var{c4}\$

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\$x=\\var{c5}\$

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\$y=\\simplify{{mfake}x+{cfake}}\$

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Bruk figuren ovenfor og sett sammen rett linje med rett likning.

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Match up equations with the corresponding lines on a graph.

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