Question

Find the equation of the line that is passing through (8, -2) and parallel to the line passing through (-3, -2) and (5, 1).

Answer 1

Let the points are (x₁, y₁) = (- 3, - 2) and (x₂, y₂) = (5, 1).

Slope m = [(y₂ - y₁)/(x₂ - ₁)]

m = [(1 - (- 2))/(5 -(- 3))]

m = [(1 + 2)/(5 + 3)]

m = 3/8.

Therefore slope of line through these points is 3/8.

If two lines are parallel, then they have the same slope.

So, the parallel line through (8, - 2) has a slope of 3/8.

Now, the line equation is y = 3/8x + b.

To find the y - intercept, substitute the values of (x, y ) = (8, - 2) and m = 3/8 in the slope - intercept from of equation y = mx + b and solve for b.

- 2 = 3/8 * 8 + b

b = - 3 - 2 = - 5.

Substitute the values of m = 3/8 and b = - 5 in the slope - intercept form of equation.

y = mx + b ⇒ y = (3/8)x - 5.

The equation of parallel line is y = (3/8)x - 5.