+1 vote

# What is the equation of a line through (-2,5) and whose segment intercepted between the axes in 2nd quadrant?

is equal to 7 square root of 2.

+1 vote

Point (x, y) = (-2, 5)

Given the intercept is c =7√2

point (x, y) and y intercept is c then the line equation is y = mx + c

Substitute (x, y) = (-2, 5) and c = 7√2 in the equation.

5 = m(-2) + 7√2

Subtract 7√2 from each side.

5 - 7√2 = -2m + 7√2 - 7√2                              (Simplify)

5 - 7√2 = - 2m

Divide each side by -2

(5 - 7√2) / (-2) = (-2m) / (-2)                        (Simplify)

(7√2 - 5) / 2 = m

There fore slope m = (7√2 - 5) / 2

Recall: point (x₁, y₁) and slope m then the line equation is (y - y₁) = m(x - x₁)

Given the point is (-2, 5) and slope m = (7√2 - 5) / 2 substitute above formula

Then ⇒ (y - 5 ) = [(7√2 - 5) / 2] (x - (-2))

⇒ (y - 5 ) = [(7√2 - 5) / 2] (x + 2)

Multiply each side by 2.

⇒ (y - 5 ) 2= [(7√2 - 5) / 2] (x + 2) (2)                                (Simplify)

⇒ 2 (y - 5) = (7√2 - 5)(x + 2)

Applyn distributive property a(b - c) = ab - ac.

⇒ 2(y) - 2(5) = 7√2(x) + 7√2(2) - 5(x) - 5(2)

2y - 10 = 7√2(x) + 14√2 - 5x - 10

2y - 10 + 10 = 7√2(x) + 14√2 - 5x - 10 + 10

2y = 7√2(x) + 14√2 - 5x

2y = (7√2 - 5)x + 14√2

Divide each side by 2.

2y / 2 = [ (7√2 - 5)x + 14√2] / 2                           (Simplify)

y = (1/2)(7√2 - 5)x + (14√2) / 2                              (Simplify)

y = (1/2)(7√2 - 5)x + 7√2

The line equation is y = (1/2)(7√2 - 5)x + 7√2