How do you determine the the missing coordinate of A(_, 0), B(5, 10) if the slope is 2?

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Answer 1 · 2015-06-13T21:15:36

#x_1=0#

Consider that the slope #m# is:
#m=(Deltay)/(Deltax)=(y_2-y_1)/(x_2-x_1)#
In your case:
#m=2=(10-0)/(5-x_1)#
so that rearranging:
#x_1=0#

Answer 2 · 2015-06-13T21:20:37

Let #(x_1, y_1) = A = (x_1, 0)# and #(x_2, y_2) = B = (5, 10)#

Then slope #2 = m = (Delta y)/(Delta x) = (y_2 - y_1) / (x_2 - x_1) = (10-0)/(5-x_1) = 10/(5-x_1)#

Hence #x_1 = 0#

Slope #m# is given by the formula:

#m = (Delta y)/(Delta x) = (y_2 - y_1)/(x_2 - x_1)#

where the line passes through points #(x_1, y_1)# and #(x_2, y_2)#

In our example, we are given #m#, #y_1#, #x_2# and #y_2# and we are trying to find the value of #x_1#.

Putting our known values into the equation for slope, we get:

#2 = (10-0)/(5-x_1) = 10/(5-x_1)#

Multiply both ends by #(5-x_1)# to get:

#10 = 2(5 - x_1) = 10 - 2x_1#

Subtract #10# from both sides to get:

#-2x_1 = 0#

Divide both sides by #-2# to get:

#x_1 = 0#