Question

What is the equation of the line through (5,1) with a slope of -3?

a. y+1 = 3(x+5)
b. y-1 = 3(x-5)
c. y-1 = -3(x-5)
d. y+1 = -3(x-5)

Answer 1

c.y-1 = -3(x-5)

Explanation:

We have given slope of a line and the point that is passing through the line.

slope = -3 and (x₁,y₁) = (5,1)

We have to find the equation of line.

y-y₁ = m(x-x₁) is point-slope form of the equation of line where m is slope.

Putting given values in above formula, we have

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

y-1 = -3(x-5) is the equation of the line through (5,1) with a slope of -3.

Answer 2

C

Explanation:

The equation of a line is given by the formula
`y-y_1=m(x-x_1)`

Where
`x_1` is the x-coordinate (it is given as 5)

`y_1` is the y-coordinate (it is given as 1), and

m is the slope (it is given as -3)

Plugging in all the info into the formula we have:

`y-y_1=m(x-x_1)\\y-1=-3(x-5)`

From the answer choices, we see that C is the correct answer.