A line passes through #(5 ,1 )# and #(6 ,5 )#. A second line passes through #(4 ,3 )#. What is one other point that the second line may pass through if it is parallel to the first line?
1 Answer
Explanation:
So the steps are find the gradient of the first line (it will be the same gradient in the second line as it is parallel) then write the second line in the from
#y = ax + b#
(where
Step 1. Gradient
#m = (y_1-y_2) / (x_1-x_2)#
#m = (1 - 5) / (5 - 6) -># (from the first two points)
#"gradient" = 4#
Step 2. Equation
Second line's equation is
Solve for
#3 = 4 (4) + b#
#b = 3-16#
#b= -13#
Hence the equation is
#y = 4x -13#
Step 3. Find point
Next we find a point. Let
#y = 4 (1) - 13#
#y = -9#
so the point is