What is the equation of the line passing through the points #(-5, 14)# and #(4, -4)#?

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Answer 1 · 2018-04-12T02:17:52

#y=-2x+4#

Use the slope formula:

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

Given #(-5,14)# and #(4,-4)#

Let:

#(color(red)(-5),color(blue)(14))->(color(red)(x_1),color(blue)(y_1))#

#(color(red)(4),color(blue)(-4))->(color(red)(x_2),color(blue)(y_2))#

Substituting in for the slope formula...

#m=color(blue)(-4-14)/color(red)(4-(-5))=color(blue)(-18)/color(red)(9)=-2#

Now that we have the slope #m#, we can find the equation of the line by using the point-slope formula:

#y-y_1=m(x-x_1)#

Note: #(x_1,y_1)# can be either point given. I'll use the point #(4,-4)#

So...

#y-(-4)=-2(x-4)#

#y+4=-2(x-4)#

We can then rewrite this equation in #y=mx+b# form by simply solving for #y#

Doing so, one gets,

#y=-2x+4#