What is the slope and intercept of #y-(-4)=-1(x-6)#?

2 Answers
Aug 3, 2018

Answer:

Slope: -1

x-intercept: (2, 0)

y-intercept: (0, 2)

Explanation:

#y - (-4) = -1(x-6)#

We know that the equation is in point-slope form:
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Therefore, we know that the slope is #-1#.

To find the #x#-intercept, plug in #0# for #y# and solve for #x#:
#0 - (-4) = -1(x-6)#

#4 = -x + 6#

#-2 = -x#

#x = 2#

The #x#-intercept is at #(2, 0)#.

To find the #y#-intercept, plug in #0# for #x# and solve for #y#:
#y - (-4) = -1(0-6)#

#y + 4 = -1(-6)#

#y + 4 = 6#

#y = 2#

The #y#-intercept is at #(0, 2)#.

Hope this helps!

Aug 4, 2018

Answer:

Slope #-1#, #x#-int #2# and #y#-int #2#

Explanation:

Our equation is in point-slope form

#y-y_1=m(x-x_1)#, where slope #m# and points (#x_1,y_1#).

We immediately see that our slope is #-1#. We can find the #y#-intercept by converting this to slope intercept form

#y=mx+b#, with slope #m# and a #y#-intercept of #b#.

Our equation simplifies to

#y+4=-1(x-6)#

We can distribute the negative on the right to get

#y+4=-x+6#

Lastly, we can subtract #4# from both sides to get

#y=-x+2#

We see that our #y#-intercept is #2#. What about the #x#-intercept? This can easily be found by setting #y# equal to zero.

#-x+2=0=>-x=-2=>x=2#

Therefore, our slope is #-1#, our #y#-intercept is #2#, and so is our #x#-intercept.

Hope this helps!