What is the equation of the line between #(-9,16)# and #(-4,12)#?

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Answer 1 · 2018-04-16T01:21:52

#(-9,16)# and #(-4,12)#

Let's use the point-slope formula

#(y_2-y_1)/(x_2-x_1)#

#(12-16)/(-4--9)#

#(color(green)(-4))/color(blue)(5#

Now we have the slope for point-slope form, which is #y =mx+b# with #m# being the slope and #b# as the #y#-intercept, the value of #x# when #y=0#

Let's guess:

#y=-4/5x+5#
graph{y=-4/5x+5}

Were looking for #(-4, 12)#

Nope, not quite

#y=-4/5x+5.2#
graph{y=-4/5x+5.2}

Almost

#y=-4/5x+7.8#
graph{y=-4/5x+7.8}

We're so close

#y=-4/5x+8.8#
graph{y=-4/5x+8.8}

Great! We have our equation!

#y=-4/5x+8.8#