Question 116687
#1


{{{x=2y-7}}} Start with the given equation


{{{x+7=2y}}} Add 7 to both sides



{{{(1/2)x+7/2=y}}}Divide both sides by 2


So the equation in y form is {{{y=(1/2)x+7/2}}}


Let's use the general equation {{{y=mx+b}}} where m is the slope and b is the y-intercept


From {{{y=(1/2)x+7/2}}}, we can see that {{{m=1/2}}} and {{{b=7/2}}} 


So the slope is {{{m=1/2}}} and the y-intercept is {{{b=7/2}}}



Notice if we graph {{{y=(1/2)x+7/2}}} we can see that the slope is {{{m=1/2}}} and the y-intercept is {{{b=7/2}}}. So this visually verifies our answer.



{{{ graph( 500, 500, -10, 10, -10, 10, (1/2)x+7/2) }}}



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#2


Let's use the general equation {{{y=mx+b}}} where m is the slope and b is the y-intercept


From {{{y=(1/4)x+3}}}, we can see that {{{m=1/4}}} and {{{b=3}}} 


So the slope is {{{m=1/4}}} and the y-intercept is {{{b=3}}}


Notice if we graph {{{y=(1/4)x+3}}} we can see that the slope is {{{m=1/4}}} and the y-intercept is {{{b=3}}}. So this visually verifies our answer.




{{{ graph( 500, 500, -10, 10, -10, 10, (1/4)x+3) }}}