what line does (4,5) and (-3,-2) go through

Question

Trying to find the slope of the line.

Answer 1

Given points say (x1, y1) = (4, 5)

                       (x2,y2) = (-3, -2)

Slope of he line m = (y2-y1)/(x2-x1).

= (- 2 - 5)/( - 3 - 4)

= - 7 / - 7

= 1

Line equation is y-y1 = m(x-x1)

y - 5 = 1(x - 4)

y - 5 = x - 4

Add 5 to each side.

y - 5 + 5 = x  - 4 + 5

Required line equation is y = x + 1.

 

Answer 2

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

Let the points are (x₁, y₁) = (4, 5) and (x₂, y₂) = (- 3, -2).

Slope (m) = [(y₂ - y₁)/(x₂ -x₁)]

m = [(- 2 - 5)/(-3 - 4)]

m  = [- 7/- 7]

⇒ m = 1.

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

Find the y - intercept by substituting any point in the line equation say (x, y) = (4, 5).

5 = (1)(4) + b

b = 5 - 4

⇒ b = 1.

The line equation is y = x + 1.