Question

Line A has a slope of -1/6 and passes through the point 3, 7 2/3

Line B has a slope of 1/2 and passes through the point -17, -1

Find the point where line A intersects line B.

Answer 1

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).