Question

Use exact numbers. Complete the equation of the line through ( 2 , 1 ) (2,1)left parenthesis, 2, comma, 1, right parenthesis and ( 5 , − 8 ) (5,−8)left parenthesis, 5, comma, minus, 8, right parenthesis.

Answer 1

y - 1 = -3(x - 2)

Explanation:

Sounds as though you want the equation of the line through (2, 1) and (5, -8).

As we move from (2, 1) to (5, -8), x (the "run") increases by 3 and y (the "rise") decreases by 9. Thus, the slope of this line is m = rise / run = -9/3, or m = -3.

Let's use the point-slope formula for a straight line here: The point (h, k) is (2, 1) and the slope is -3. Then y - k = m(x - h) becomes:

y - 1 = -3(x - 2)

Answer 2

y = - 3x + 7

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 =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (2, 1) and (x₂, y₂ ) = (5, - 8)

m =
`(-8-1)/(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 = 7

y = - 3x + 7 ← equation of line