Question

2.) Use the Slope Intercept Form of a line to find the equation of the line from point C to point D.

Slope Intercept Form of a Line:

y = mx + b

m is the slope and b is the y-intercept

Answer 1

First we need slope

• C=(0,0)
• D(7,12)

`\\ \sf\longmapsto m=(12-0)/(7-0)`

`\\ \sf\longmapsto m=(12)/(7)`

Put D co-ordinates on y=mx+b

`\\ \sf\longmapsto 12=(12)/(7)(7)+b`

`\\ \sf\longmapsto 12=12+b`

`\\ \sf\longmapsto b=12-12`

`\\ \sf\longmapsto b=0`

Now

slope intercept form.

`\\ \sf\longmapsto y=(12)/(7)x`

• As b=0

Answer 2

• General equation of a line:

`{ \rm{y = mx + b}}`

Consider end points of line CD: (0, 0) and (7, 12):

• find the slope, m:

`{ \rm{slope = (y _(2) - y _(1) )/(x _(2) - x _(1) ) }} \\ \\ { \tt{m = (12 - 0)/(7 - 0) }} \\ \\ { \underline{ \tt{ \: \: m = (12)/(7) \: \: }}}`

• using end point (0, 0), find the y-intercept, b:

`{ \rm{y = mx + b}} \\ \\ { \rm{0 = ( (12)/(7) * 0) + b}} \\ \\ { \tt{b = 0}}`

• therefore, equation of line CD is;

`{ \boxed{ \boxed{ \tt{ \: \: y = (12)/(7)x \: \: }}}}`