A line passes through #(2 ,3 )# and #( 6, 2 )#. A second line passes through #( 7, 4 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Jade
Oct 5, 2016

Any set of points you put into that equation, should be parallel to the first line.

Explanation:

If two lines are parallel to each other, then they have the same slope. To find the slope of the first line, use point slope formula: #m = (y_2 - y_1)/(x_2 - x_1)# where #m# is the slope

#(2,3) and (6,2)# corresponds to #(x_1, y_1) and (x_2,y_2)#

Plug the numbers into the formula

#m= (2-3)/(6-2) = -1/4#

So, the slope is #-1/4#

Next, find the equation of the second line using this form:
#y=mx+b#, where #m# is the slope, which is #-1/4#

#y=-1/4x+b#

Now, to find #b#, which is the y-intercept, plug in the coordinates #(7,4)# into the y and x intercepts

#4=-1/4(7) +b#
#4=-7/4+b#
#23/4=b#

So, the equation should look like #y=-1/4x + 23/4#

Any set of points you put into that equation, should be parallel to the first line.

For example, if you put 0 in for x and solve, your y would be #23/4# so the points would be #(0,23/4)#

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