Question

C(-5, -2); slope = 1/4.

Answer 1

Slope (m) =1/4  and the point is C(- 5, - 2).

Line equation is : y - y₁ = m(x - x₁).

Substitute the values of C(x₁, y₁) = (- 5, - 2) and m = 1/4 in y - y₁ = m(x - x₁).

y + 2 = 1/4(x + 5)

Subtract 2 from each side.

y  = 1/4(x + 5) - 2

Apply distributive property : a(b + c) = ab + ac.

y  = (1/4)x + (5/4) - 2

y  = (1/4)x  - 3/4.

The slope - intercept form of the line is y  = (1/4)x  - 3/4.

Comments

Point - slope - form of a line equation is y - y₁ = m(x - x₁), where m is slope, and (x₁, y₁) is the point lies on the line.