The graph of the equation y = mx + c passes through the points (1, 4) and (-2, -5). Determine the values of m and c.

Since, (1, 4) and (-2, -5) lie on y = mx + c hence, the points must satisfy the equation.

Putting (1, 4) in the equation,

⇒ 4 = m(1) + c
⇒ 4 = m + c
⇒ m = 4 - c      (Eq 1)

Putting (-2, -5) in the equation,

⇒ -5 = m(-2) + c
⇒ -5 = -2m + c.

Putting value of m from Eq 1 in above equation,

⇒ -5 = -2(4 - c) + c
⇒ -5 = -8 + 2c + c
⇒ -5 + 8 = 3c
⇒ 3 = 3c
⇒ c = 1.

Putting value of c in Eq 1,

⇒ m = 4 - 1
⇒ m = 3.

Hence, the value of m = 3 and c = 1.