How do you write an equation in slope intercept form given (2, 4) and (1, –3)?

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Answer 1 · 2017-11-21T10:43:47

#y=7x-10#

See the explanation for the process.

First determine the slope using the slope formula:

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

where:

#m# is the slope, #(x_1,y_1)# is one point, and #(x_2,y_2)# is the second point.

Point 1: #(2,4)#

Point 2: #(1,-3)#

Plug the known values into the formula:

#m=(-3-4)/(1-2)#

Simplify.

#m=(-7)/(-1)# #larr# two negatives make a positive

#m=7#

Now determine the linear equation using the point-slope form:

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

where #y_1# and #x_1# are a point, and #m=7#

We can use one of the points from determining the slope. I'm going to use Point 1: #(2,4)#.

Plug in the given point and slope.

#y-4=7(x-2)# #larr# point-slope form

We can solve the point-slope form for #y#, which will give us the slope-intercept from:

#y=mx+b#,

where:

#m# is the slope and #b# is the y-intercept.

#y-4=7(x-2)#

Expand.

#y-4=7x-14#

Add #4# to both sides.

#y=7x-14+4#

Simplify.

where the slope #(m)# is #7# and the y-intercept #(b)# is #-10#.