Question

21. Plot the graphs of the given equations.
a) y = x-2 b) y = 2x – 8

Answer 1

                            Plot the graphs of the given equations.

Part a)

Given the equation

$y\:=\:x-2$

Determining x-intercept:

$\mathrm{x-intercept\:is\:a\:point\:on\:the\:graph\:where\:}y=0$

$x-2=0$

$\mathrm{Add\:}2\mathrm{\:to\:both\:sides}$

$x-2+2=0+2$

$x=2$

So x-intercept is (2, 0)

Determining x-intercept:

$y\mathrm{-intercept\:is\:the\:point\:on\:the\:graph\:where\:}x=0$

$y=0-2$

$\mathrm{Subtract\:the\:numbers:}\:0-2=-2$

$y=-2$

So y-intercept is (0, -2)

Also

$\mathrm{Slope\:of\:}x-2:\quad m=1$

The graph of the equation is attached below, where red line indicates the graph of the equation $y\:=\:x-2$.

Part b)

Given the equation

$y\:=\:2x\:-\:8$

Determining x-intercept:

$\mathrm{x-intercept\:is\:a\:point\:on\:the\:graph\:where\:}y=0$

$2x-8=0$

$\mathrm{Add\:}8\mathrm{\:to\:both\:sides}$

$2x-8+8=0+8$

$2x=8$

$\mathrm{Divide\:both\:sides\:by\:}2$

$\frac{2x}{2}=\frac{8}{2}$

$x=4$

So x-intercept is (4, 0)

Determining x-intercept:

$y\mathrm{-intercept\:is\:the\:point\:on\:the\:graph\:where\:}x=0$

$y=2\cdot \:0-8$

$\mathrm{Apply\:rule}\:0\cdot \:a=0$

$y=0-8$

$\mathrm{Subtract\:the\:numbers:}\:0-8=-8$

$y=-8$

So y-intercept is (0, -8)

Also

$\mathrm{Slope\:of\:}2x-8:\quad m=2$

The graph of the equation is attached below, where blue line indicates the graph of the equation $y\:=\:2x\:-\:8$.