Find an equation of the line passing through the points (-2,4) and ( 1,2). show your work. you!

The typical equation of a line is: y = mx + b → where m: slope and where b: y-intercept

Equation of the line (ℓ1):

y = (3/4)x + 5 → the slope is (3/4)

Two lines are perpendicular if the product of their slope is: - 1

slope_ ℓ1 * slope_ ℓ2 = - 1

slope_ ℓ2 = - 1/slope_ ℓ1 → you know that: slope_1 = (3/4)

slope_ ℓ2 = - 1/(3/4)

slope_ ℓ2 = - 4/3 → so, the slope of the line (ℓ2) is: - 4/3

Recall: the typical equation of a line is: y = mx + b

The equation of the line (ℓ2) becomes: y = - (4/3)x + b

You know that the lines (ℓ2) passes through the point (3 ; 5). So the coordinates of this point must verify the equation of the line (ℓ2) because this point belongs to the line (ℓ2).

y = - (4/3)x + b

b = y + (4/3)x → you substitute x and y by the coordinate of the point

b = 5 + [(4/3) * 3]

b = 5 + 4

b = 9