Question

Write an equation of the line that goes through the points (1, -2) and (3, 1).

a. y + 1 = 3/2(x - 2)
b. y + 1 = 2/3(x - 2)
c. y + 2 = 3/2(x - 1)
d. y + 2 = 2/3(x - 1)

Answer 1

The equation of the line that goes through the points (1, -2) and (3, 1) is y + 2 = 3/2(x - 1).

Step-by-step explanation:

The equation of the line that goes through the points (1, -2) and (3, 1) can be found using the slope-intercept form equation: y = mx + b. First, we need to find the slope:

m = (y2 - y1) / (x2 - x1)

m = (1 - (-2)) / (3 - 1) = 3/2

Next, we can substitute one of the points and the slope into the equation to find the y-intercept:

y = mx + b

-2 = (3/2)(1) + b

-2 = 3/2 + b

-2 - 3/2 = b

-4/2 - 3/2 = b

-7/2 = b

Therefore, the equation of the line is y + 2 = 3/2(x - 1).

Answer 2

(c)

Step-by-step explanation:

the equation of a line in point- slope form is

y - b = m(x - a)

m is the slope and (a, b ) a point on the line

calculate the slope m , using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

let (x₁, y₁ ) = (1, - 2 ) and (x₂, y₂ ) = (3, 1 )

substitute these values into the formula for m

m =
`(1-(-2))/(3-1)` =
`(1+2)/(2)` =
`(3)/(2)`

use either of the 2 given points for (a, b )

using (1, - 2 ) , then

y - (- 2) =
`(3)/(2)` (x - 1) , that is

y + 2 =
`(3)/(2)` (x - 1)