The problemTo write requires writing the equation of the the equation of the line in given slope line in-inter cepts formlope (-inter(cepty = form mx (\ +( by\ = mx)), let's + analyze b the)), where ( graphm.

Step\ )1: is Identify the two slope and $b points$ is the on the line

y-interFromcept the.

graph: 1###. Step The lower point is1 $(-:1 Identify two, -10 points)$. 2. The on upper the line From point the is graph: $(2,- The first point is \8((-)\1, -10)$. ).

-### Step 2: Calculate the The slope second point (\ is (m((\2,)) The slope $m$ is calculated using: 8)).

Step 2: Calculate the[

slopem m = \ fracThe{ slopey formula_ is2 -: \ y_[ m1 =}{ \xfrac_{2y -_ x2_ -1 y} _\1] }{Subxstit_uting2 the - points x _((-11,} -] 10Sub))stit anduting the \ points(( \2,((-1 ,8 -)\10): ))[ andm \ =(( \2frac,{8 8 -)\ (-): 10)}[ {m2 = - (- \1frac{8)} = \ - (-frac10{)}8{ +2 -10 (-}{12)} + = \frac{8 + 110}}{ =2 \ +frac {118}}{ =3 }frac ={ 186}{ 3}]

=### Step6 3:] UseThus the, slope -intercept form (\m(y = mx = + b6\.

))### to find Step $3b:$ Substitute $m = 6$ and one Find the of y-intercept the $b$ Using the slope-intercept form points intoy = the equation mx. + Using b \,((- substitute1 one, of - the10 points)\ (): \e[ .gy., = \ mx(( +2 b, \ im8plies)\ -))10 and = the slope $m = 6$: [ 68(- =1 )6 +( b2 )\ +] b
[ -] 10\ =[ -86 = + b12 \ +im bplies b\ =] -\10[ +b =6 =8 - -4 12\ =]

-###4 Step \4]

:### Write Step the equation The equation of the line is: [ y =4: Write the equation The 6x - equation of4 the\ line]

is: Would you\ like[ y further = 6 clarification orx additional details?

4### \ Follow]

-up questionsWould: you like additional details or clarification?

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How do you verify the slope using other### Relative points Questions: on1 the. How line do? you2 verify. the Can the slope using other slope points-inter oncept the equation line be? rearr2anged. into Can standard the form equation? 3. be How written in other forms (e would you.g graph a., line standard given its slope form-inter)? cept3 equation? .4 What. changes What in the equation if the does line the shifts y up-inter orcept down represent? in4 the. graph? 5. How do parallel lines relate in terms How of do you handle a vertical slope or horizontal?

line###'s equation Tip: ? 5Always. verify Can you use the slope by a point selecting different other pairs of than points \ on(( the2 line, to confirm consistency8).) to find $b$?

Tip:

Always double-check the slope calculation to ensure the equation accurately represents the line.