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.
\nThe 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 $x$.
\nThe $y$-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).
\nWe 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.
\nA:
\n$y=\\simplify{{m1}x+{c1}}$ gives us $m=\\var{m1}$ and $c=\\var{c1}$.
\nB:
\n$y=\\simplify{{m2}x+{c2}}$ gives us $m=\\var{m2}$ and $c=\\var{c2}$.
\nC:
\n$y=\\simplify{{m3}x+{c3}}$ gives us $m=\\var{m3}$ and $c=\\var{c3}$.
\nD:
\n$y=\\simplify{{c4}}$ gives us $m=0$ and $c=\\var{c1}$.
\nE:
\n$x=\\var{c5}$ 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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