Question

A line which join the point A (3, k) and B (-2, 5) is parallel to another line whose equation is 5y + 2x =10
Find the value of K.

Answer 1

To determine the value of k, we need to find the equation of the line passing through points A and B and then compare it to the given equation.

The equation of a line passing through two points (x₁, y₁) and (x₂, y₂) can be found using the slope-intercept form: y - y₁ = m(x - x₁), where m is the slope of the line.

Slope (m) = (y₂ - y₁) / (x₂ - x₁)

Using points A(3, k) and B(-2, 5), the slope of the line passing through A and B is:

m = (5 - k) / (-2 - 3) = (5 - k) / -5

Since the line is parallel to the given line with equation 5y + 2x = 10, the slopes of the two lines must be equal.

Therefore, the slope of the given line is -2/5.

Setting the slopes equal:

-2/5 = (5 - k) / -5

Cross-multiplying and solving for k:

-2 * -5 = (5 - k) * -5
10 = -25 + 5k
35 = 5k
k = 7

Therefore, the value of k is 7.