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

a. y + 9 = −(x − 1)

b. y − 9 = 1(x + 1)

c. y + 9 = 1(x + 1)

d. y − 9 = −(x − 1)

The equation of point-slope formula is used to find the equation of a line when we know the slope of the line and a point on the line are known.

Answer: d. y − 9 = −(x − 1)

Let's Solve.

Explanation:

Point slope formula: y - y₁ = m (x - x₁) ----------- (1)

⇒ m = slope (x1, y1) 

To begin, we must use the slope formula to determine the slope: y₂ - y₁/ x₂ - x₁ = Slope

Given two coordinates, solve for:

(1, 9) and (−1, 11)

Fill in the values in the slope formula:

⇒ Slope = 11 - 9 / -1 -1

⇒ 2 / -2 = -1

Now we know that: 

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

Put the values in equation (1), we get

(y - 9) = -1(x - 1) 

The equation in point-slope form of the line passing through (1, 9) and (−1, 11) is y − 9 = −(x − 1)