Question

What is the equation in point-slope form of the line passing through (1,9) and (-1, 11)? (6 points)

Oy+9= -(x-1)
Oy-9=1(x+1)
Oy+9=1(x+1)
Oy-9=-(x-1)

Answer 1

Explanation:

Point slope form:

y-y1=m(x-x1)

m=slope

(x1,y1)

First we need to find the slope using the slope formula:

y2-y1/x2-x1= slope

Given the two coordinates:

(1, 9) and (−1, 11)

Plug them into the slope formula:

11-9=2/-1-1=-2

Simplify:

2/-2=-1

Now we know that:

m=-1 and the (x1,y1) would be (1, 9)

Now we simply plug in the info:

y-9=-(x-1)

Final answer: y − 9 = −(x − 1)

Answer 2

`\sf D. \quad y-9=-(x-1)`

Explanation:

First, find the slope of the line passing through the given points (1, 9) and (-1, 11):

• 
  `\sf \textsf{let}\:(x_1,y_1)=(1,9)`

• 
  `\sf \textsf{let}\:(x_2,y_2)=(-1,11)`

`\implies \sf \textsf{slope}\:(m)=(y_2-y_1)/(x_2-x_1)=(11-9)/(-1-1)=-1`

Point-slope form of linear equation

`\sf y-y_1=m(x-x_1)`

where:

• m is the slope
• (x₁, y₁) is a point on the line

Substitute the found slope and the point (1, 9) into the formula:

`\implies \sf y-9=-1(x-1)`

`\implies \sf y-9=-(x-1)`