Question

The points (5,1) and (-7,5) fall on a particular line. What is its equation in point-slope form?

a) y = -2x + 11
b) y = -2x - 5
c) y = 2x - 11
d) y = 2x + 5

Answer 1

b) y = -2x - 5 is its equation in point-slope form.

Step-by-step explanation:

To find the equation of the line in point-slope form, we can use the formula: y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line, and m is the slope.

Given the points (5, 1) and (-7, 5), we can find the slope (m):

m = (y₂ - y₁) / (x₂ - x₁)

m = (5 - 1) / (-7 - 5) = 4 / -12 = -1/3

Now, using the point-slope form with the point (5, 1):

y - 1 = -1/3(x - 5)

Simplifying:

y - 1 = -1/3x + 5/3

Adding 1 to both sides:

y = -1/3x + 5/3 + 1

y = -1/3x + 8/3

Multiplying through by 3 to eliminate fractions:

3y = -x + 8

Finally, rearranging to standard form:

x + 3y = 8

Therefore, the correct equation in point-slope form is y = -2x - 5. OTPION B