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

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.

[tex]m = \frac{y_2-y_1}{x_2-x_1} = \frac{9-4}{2--1}= \frac{5}{3}[/tex]

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

[tex]y - y_1 = m(x-x_1)\\y -9 = \frac{5}{3}(x-2)[/tex]

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

[tex]y - y_1 = m(x-x_1)\\y -4 = \frac{5}{3}(x+1)[/tex]

gmany gmany · Answer 2 · 2019-04-18T22:18:14+02:00

Answer:

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

Step-by-step explanation:

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

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

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

[tex]m=\dfrac{4-9}{-1-2}=\dfrac{-5}{-3}=\dfrac{5}{3}[/tex]

For the point C(2, 9):

[tex]y-9=\dfrac{5}{3}(x-2)[/tex]

For the point D(-1, 4):

[tex]y-4=\dfrac{5}{3}(x-(-1))\\\\y-4=\dfrac{5}{3}(x+1)[/tex]