What is the equation of the line passing through the points (-3,8) and (-4,-5)

Question

A)y=13x-47
B)y=13x+47
C)y=13x-31
D)y=-13x-31
Please show me all your work so that I can learn how to do this..thanks

Answer 1

The points are (- 3, 8) and (- 4, - 5).

Line equation formula : y - y₁ = m(x - x₁).

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

= (- 5 - 8)/(- 4 + 3)

= (- 13)/(- 1)

m = 13.

Substitute the values of (x₁, y₁) = (- 3, 8), (x₂, y₂) = (- 4, - 5), and m = 13 in Line equation formula.

y - 8 = 13(x + 3)

Add 8 to each side.

y = 13(x + 3) + 8

Apply distributive property.

y = 13x + 39 + 8

y = 13x + 47.

Line equation is y = 13x + 47.

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) = (- 3, 8) and (x₂, y₂) = (- 4, - 5).

Slope (m) = [(y₂ - y₁)/(x₂ -x₁)]

m = [(- 5 - 8)/(- 4 - (- 3))]

m  = [- 13/-1]

⇒ m = 13.

Now, the line equation is y = 13x + b.

Find the y - intercept by substituting any point in the line equation say (x, y) = (- 3, 8).

8 = (13)(- 3) + b

b = 8 + 39

⇒ b = 47.

The line equation is y = 13x + 47.

Comments

Option B is correct choice.