Intersection with the $xx$-axis

Calculate the intersection of the line with the $xx$-axis.

Set the expression for the line equation equal to 0 and solve for $xx$.

$\Rightarrow \backslash ;\backslash ;\backslash Rightarrow\backslash ;\backslash ;$ The line intersects the $xx$-axis at $S_x(1.75\mathrm{\mid }0)S\_x(1.75|0)$.

Intersection with the $yy$-axis

Calculate the intersection of the line with the $yy$-axis.

To do this, plug the value $x=0x=0$ into the expression for the straight line equation.

$y=-2\cdot 0+3.5y=-2\backslash cdot0+3.5$

$y=3.5y=3.5$

$\Rightarrow \backslash ;\backslash ;\backslash Rightarrow\backslash ;\backslash ;$ The line intersects the $yy$-axis at $S_y(0\mathrm{\mid }3.5)S\_y(0|3.5)$.

Intersection with the $xx$-axis

Calculate the intersection of the line with the $xx$-axis.

Set the expression for the line equation equal to 0 and solve for $xx$.

$\Rightarrow \backslash ;\backslash ;\backslash Rightarrow\backslash ;\backslash ;$ The line intersects the $xx$-axis at $S_x(1.4\mathrm{\mid }0)S\_x(1.4|0)$.

Intersection with the $yy$-axis

Calculate the intersection of the line with the $yy$-axis.

To do this, plug the value $x=0x=0$ into the expression for the straight line equation.

$y=5\cdot 0-7y=5\backslash cdot0-7$

$y=-7y=-7$

$\Rightarrow \backslash ;\backslash ;\backslash Rightarrow\backslash ;\backslash ;$ The line intersects the $yy$-axis at $S_y(0\mathrm{\mid }-7)S\_y(0|-7)$.

Intersection with the $xx$-axis

Calculate the intersection of the line with the $xx$-axis.

Set the expression for the line equation equal to 0 and solve for $xx$.

$\Rightarrow \backslash ;\backslash ;\backslash Rightarrow\backslash ;\backslash ;$ The line intersects the $xx$-axis at $S_x(\text{}-\frac{4}{3}-\mathrm{\mid }0)S\_x(\; -\backslash frac43-|0)$.

Intersection with the $yy$-axis

Calculate the intersection of the line with the $yy$-axis.

To do this, plug the value $x=0x=0$ into the expression for the straight line equation.

$y=\frac{3}{2}\cdot 0+2y=\backslash frac32\backslash cdot0+2$

$y=2y=2$

$\Rightarrow \backslash ;\backslash ;\backslash Rightarrow\backslash ;\backslash ;$ The line intersects the $yy$-axis at $S_y(0\mathrm{\mid }2)S\_y(0|2)$.

Intersection with the $xx$-axis

Calculate the intersection of the line with the $xx$-axis.

Set the expression for the line equation equal to 0 and solve for $xx$.

$\Rightarrow \backslash ;\backslash ;\backslash Rightarrow\backslash ;\backslash ;$ The line intersects the $xx$-axis at $S_x(6.25\mathrm{\mid }0)S\_x(6.25|0)$.

Intersection with the $yy$-axis

Calculate the intersection of the line with the $yy$-axis.

To do this, plug the value $x=0x=0$ into the expression for the straight line equation.

$y=-\frac{2}{5}\cdot 0+\frac{5}{2}y=-\backslash frac25\backslash cdot0+\backslash frac52$

$y=\frac{5}{2}=2.5y=\backslash frac\{5\}\{2\}=2.5$

$\Rightarrow \backslash ;\backslash ;\backslash Rightarrow\backslash ;\backslash ;$ The line intersects the $yy$-axis at $S_y(0\mathrm{\mid }2.5)S\_y(0|2.5)$.

To obtain a general line equation $y=m\cdot x+ty=m\; \backslash cdot\; x+t$, multiply out the bracket

$y=2(x-\frac{2}{3})y=2(x-\backslash frac23)$

$y=2x-\frac{4}{3}y=2x-\backslash frac43$

Intersection with the $xx$-axis

Calculate the intersection of the line with the $xx$-axis.

Set the expression for the line equation equal to 0 and solve for $xx$.

$\Rightarrow \backslash ;\backslash ;\backslash Rightarrow\backslash ;\backslash ;$ The line intersects the $xx$-axis at $S_x(\frac{2}{3}\mathrm{\mid }0)S\_x(\backslash frac\{2\}\{3\}|0)$.

Intersection with the $yy$-axis

Calculate the intersection of the line with the $yy$-axis.

To do this, plug the value $x=0x=0$ into the expression for the straight line equation.

$y=2\cdot 0-\frac{4}{3}y=2\backslash cdot0-\backslash frac43$

$y=-\frac{4}{3}y=-\backslash frac\; 4\; 3$

$\Rightarrow \backslash ;\backslash ;\backslash Rightarrow\backslash ;\backslash ;$ The line intersects the $yy$-axis at $S_y(0\mathrm{\mid }-\frac{4}{3})S\_y(0|-\backslash frac\{4\}\{3\})$.

Transform the equation

To obtain a general line equation $y=m\cdot x+ty=m\backslash cdot\; x+t$, swap both elements on the right side.

$y=-\frac{4}{3}-\frac{1}{2}xy=-\backslash frac43-\backslash frac12x$

$\phantom{y}=-\frac{1}{2}x-\frac{4}{3}\backslash phantom\{y\}=-\backslash frac12x-\backslash frac43$

Intersection with the $xx$-axis

Calculate the intersection of the line with the $xx$-axis.

Set the expression for the line equation equal to 0 and solve for $xx$.

$\Rightarrow \backslash ;\backslash ;\backslash Rightarrow\backslash ;\backslash ;$ The line intersects the $xx$-axis at $S_x(-\frac{8}{3}\mathrm{\mid }0)S\_x(-\backslash frac\{8\}\{3\}|0)$.

Intersection with the $yy$-axis

Calculate the intersection of the line with the $yy$-axis.

To do this, plug the value $x=0x=0$ into the expression for the straight line equation.

$y=-\frac{1}{2}\cdot 0-\frac{4}{3}y=-\backslash frac12\backslash cdot0-\backslash frac43$

$y=-\frac{4}{3}y=-\backslash frac\; 4\; 3$

$\Rightarrow \backslash ;\backslash ;\backslash Rightarrow\backslash ;\backslash ;$ The line intersects the $yy$-axis at $S_y(0\mathrm{\mid }-\frac{4}{3})S\_y(0|-\backslash frac\{4\}\{3\})$.