1 answer

How do you write the equation of a line in slope-intercept form that passes through (4, 1) and (1,-2)?

Question:

How do you write the equation of a line in slope-intercept form that passes through (4, 1) and (1,-2)?

Answers

#y=x-3#

Explanation:

Begin by finding the slope of the two points by using the slope formula: #m=(y_2-y_1)/(x_2-x_1)#

If we let #(4,1)->(color(blue)(x_1),color(red)(y_1))# and #(1,-2)->(color(blue)(x_2),color(red)(y_2))# Then,

#m=color(red)(-2-1)/(color(blue)(1-4))=-3/-3=1#

Now that we have our slope of #1# we must find our y-intercept or #b# if we are using #y=mx+b# form by substituting our slope #m# and any of the two points given and solving for b.

#1=1(4)+b#

#1=4+b#

#1-4=cancel(4-4)+b#

#-3=b#

So our final equation is #y=1x-3# or simply #y=x-3#

.

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