Question

What is the equation of the line passing through the points (2, -1) and (5, -10) in slope-intercept form?

y = -3x-5
y = -3x+5
y = 3x-5
y =3x+5​

Answer 1

y = - 3x + 5

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, - 1) and (x₂, y₂ ) = (5, - 10)

m =
`(-10+1)/(5-2)` =
`(-9)/(3)` = - 3, thus

y = - 3x + c ← is the partial equation

To find c substitute either of the 2 points into the partial equation

Using (2, - 1), then

- 1 = - 6 + c ⇒ c = - 1 + 6 = 5

y = - 3x + 5 ← equation of line

Answer 2

`m = ( - 10 + 1)/(5 - 2) = ( - 9)/(3) = - 3 \\ y + 1 = - 3( x - 2) \\ y = - 3x + 6 - 1 \\ y = - 3x + 5`

The answer is the second option.

Good luck!

Intelligent Muslim,

From Uzbekistan.