slope and intercept equation

Question

Write an equation of the line that passes through the given point
and has the given slope. Write your equation in slope-intercept form.

(4,1);m=-1/2

Answer 1

The line that passes through  given point (4,1)

here slope m =-1/2

(4,1)=( X₁, y₁)

equation is ( y-y₁) = m ( x-X₁)

(y-1) = -1/2 ( x-4)

multiple each sides by 2

2(y-1) = -2/2 (x-4)

2y-2 =-x -4

x+2y=-4+2

x+2y =-2

x+2y+2 = 0

Answer 2

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

Slope (m) = - 1/2

Now, the line equation is y = (- 1/2)x + b.

Find the y - intercept by substituting the point in the line equation say (x, y) = (4, 1).

1 = (- 1/2)(4) + b

b = 1 + 2

⇒ b = 3.

The line equation in slope - intercept - form is y = (- 1/2)x + 3.