Answer:
Explanation:
The point where two lines intersect is the solution to a system of two linear equations in two variables. To find the point of intersection, we can set the two equations equal to each other and solve for the x and y values.
First, let's find the equation of Line A using the point-slope form of a line:
y - 7 2/3 = -1/6 (x - 3)
Expanding the right side:
y - 7 2/3 = -1/6 x + 1/2
Next, let's find the equation of Line B using the point-slope form of a line:
y - -1 = 1/2 (x - -17)
Expanding the right side:
y + 1 = 1/2 x + 8 1/2
Now, we set the two equations equal to each other to find the point of intersection:
y - 7 2/3 = y + 1
Solving for y:
8 5/6 = y
Now that we have y, we can substitute it back into either of the original equations to find x:
y - 7 2/3 = -1/6 x + 1/2
8 5/6 - 7 2/3 = -1/6 x + 1/2
1 1/6 = -1/6 x + 1/2
Expanding the right side:
1 1/6 = -1/6 x + 1/2
Multiplying both sides by 6:
7 = -x + 3
Adding x to both sides:
7 + x = 3
Solving for x:
x = -4
So the point where Line A and Line B intersect is (-4, 8 5/6).