Question

Consider the line containing the points C(2,9) and D(−1,4).

A: What is the slope of the line?
B: What is the equation of the line in point-slope form?

Select one answer choice for question A, and select all correct answer choices for question B.

A: −35
B: y+4=35(x−1)
B: y+9=−35(x+2)
A: −53
B: y−9=35(x−2)
B: y−9=−53(x−2)
A: 53
B: y−9=53(x+2)
B: y−4=35(x+1)
B: y−9=53(x−2)
B: y−4=53(x+1)
A: 35

Answer 1

5/3 and y -9 = 5/3(x - 2)

5/3 and y - 4 = 5/3(x + 1)

Explanation:

To write the equation of a line, calculate the slope between points (2,9) and (-1,4). After, substitute the slope and a point into the point slope form.

`m = (y_2-y_1)/(x_2-x_1) = (9-4)/(2--1)= (5)/(3)`

Substitute m = 5/3 and the point (2,9) into the point slope form.

`y - y_1 = m(x-x_1)\\y -9 = (5)/(3)(x-2)`

You could choose to use the other point (-1,4). Repeat the same process substituting m = 5/3 and the point (-1,4).

`y - y_1 = m(x-x_1)\\y -4 = (5)/(3)(x+1)`

Answer 2

`\large\boxed{m=(5)/(3)}\\\boxed{y-9=(5)/(3)(x-2)}\\\boxed{y-4=(5)/(3)(x+1)}`

Explanation:

The point-slope form of an equation of a line:

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

m - slope

The formula of a slope:

`m=(y_2-y_1)/(x_2-x_1)`

We have the points C(2, 9) and D(-1, 4). Substitute:

`m=(4-9)/(-1-2)=(-5)/(-3)=(5)/(3)`

For the point C(2, 9):

`y-9=(5)/(3)(x-2)`

For the point D(-1, 4):

`y-4=(5)/(3)(x-(-1))\\\\y-4=(5)/(3)(x+1)`