Question

Use the information to answer the question.

Information
Line A passes through the point 0 comma 5 and the point 4 comma 13. Line B passes through the point 0 comma 2 and the point 5 comma 17.

Question
At what point do the two lines intersect? Enter the answer in each box.

Response area with 2 text input boxes
(
,
)

Answer 1

To find the intersection of the two lines A and B, we first need to determine their equations.

**Line A:**
Given points: (0, 5) and (4, 13)

1. Calculate the slope (m) of Line A:
\[
m_A = \frac{y_2 - y_1}{x_2 - x_1} = \frac{13 - 5}{4 - 0} = \frac{8}{4} = 2
\]

2. Using the point-slope form \( y - y_1 = m(x - x_1) \) with point (0, 5):
\[
y - 5 = 2(x - 0)
\]
\[
y = 2x + 5
\]

**Line B:**
Given points: (0, 2) and (5, 17)

1. Calculate the slope (m) of Line B:
\[
m_B = \frac{y_2 - y_1}{x_2 - x_1} = \frac{17 - 2}{5 - 0} = \frac{15}{5} = 3
\]

2. Using the point-slope form with point (0, 2):
\[
y - 2 = 3(x - 0)
\]
\[
y = 3x + 2
\]

Now, we have the equations for the two lines:
- Line A: \( y = 2x + 5 \)
- Line B: \( y = 3x + 2 \)

To find the intersection, we set the equations equal to each other:
\[
2x + 5 = 3x + 2
\]

Solving for x:
\[
5 - 2 = 3x - 2x
\]
\[
3 = x
\]

Substituting \( x = 3 \) back into either equation (we'll use Line A):
\[
y = 2(3) + 5 = 6 + 5 = 11
\]

Thus, the intersection point is \( (3, 11) \).

**Final answer:**
(3, 11)