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)

$\\ \sf\longmapsto m=\dfrac{12-0}{7-0}$

$\\ \sf\longmapsto m=\dfrac{12}{7}$

Put D co-ordinates on y=mx+b

$\\ \sf\longmapsto 12=\dfrac{12}{7}(7)+b$

$\\ \sf\longmapsto 12=12+b$

$\\ \sf\longmapsto b=12-12$

$\\ \sf\longmapsto b=0$

Now

slope intercept form.

$\\ \sf\longmapsto y=\dfrac{12}{7}x$

• As b=0

Answer 2

Answer:

• General equation of a line:

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

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

• find the slope, m:

${ \rm{slope = \frac{y _{2} - y _{1} }{x _{2} - x _{1} } }} \\ \\ { \tt{m = \frac{12 - 0}{7 - 0} }} \\ \\ { \underline{ \tt{ \: \: m = \frac{12}{7} \: \: }}}$

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

${ \rm{y = mx + b}} \\ \\ { \rm{0 = ( \frac{12}{7} \times 0) + b}} \\ \\ { \tt{b = 0}}$

• therefore, equation of line CD is;

${ \boxed{ \boxed{ \tt{ \: \: y = \frac{12}{7}x \: \: }}}}$