write an equation in slope-intercept form for the that passes through (4,3) and (3,9)

Question

Slope intercept from for a line that passes through points.

Answer 1

Slope intercept form of a line is y  = mx + b .

Let the given points

Line equation through the two points is

y - 3 = -6x + 24

Add 3 to each side.

Required line equation y  = -6x + 27.

Answer 2

The points are (4, 3) and (3, 9).

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

Slope (m ) = (y ₂ - y ₁)/(x ₂ -x ₁).

Substitute the values of (x ₁, y ₁) = (4, 3) and (x ₂, y ₂) = (3, 9) in m = (y ₂ - y ₁)/(x ₂ -x ₁).

m = (9 -  3) / (3 - 4)

m = 6 /(- 1)

⇒ m = - 6.

Substitute the values of m = - 6 and (x, y ) = (4, 3) in slope - intercept - form of a line equation : y = mx + c.

3 = (- 6)(4) + c

3 = - 24 + c

⇒ c = 3 + 24 = 27.

Substitute the values of m = - 6 and c = 27 in slope - intercept - form of a line equation : y = mx + c.

y = (- 6)x + 27.

Therefore, slope - intercept - form of a line equation through the given points is y = - 6x + 27.