Find the equation for a line which passes through the points (2, 5) and (4, –7)

Question

Write the equation in slope intercept form

Answer 1

The points are (2, 5) and (4, - 7).

slope - intercept - form of a line equation  : y = mx + b, where m is slope and b is y - intercept.

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substitute the values of (x₁, y₁) = (2, 5) and (x₂, y₂) = (4, - 7) in m = (y₂ - y₁)/(x₂ - x₁).

= (- 7 - 5)/( 4 - 2)

= (- 12)/(2)

m = - 6.

Substitute the values of (x, y) = (2, 5) and m = - 6 in slope - intercept - form of a line equation.

5 = (- 6)(2) + b

b = 5 + 12

→ b = 17.

Substitute the values b = 17 and m = - 6 in slope - intercept - form of a line equation.

y = (- 6)x + 17.

The slope - intercept - form of a line equation is  y = - 6x + 17.