Question

Find the equation of the linear function passing through the points (1,2) and (4,11).

A) y = (3/1)x - 1
B) y = (9/2)x - (5/2)
C) y = 3x - 1
D) y = (5/2)x + (1/2)

Answer 1

C

Step-by-step explanation:

the equation of a line (linear function) in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate slope m , using the slope formula

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

let (x₁, y₁ ) = (1, 2 ) and (x₂, y₂ ) = (4, 11 )

substitute these values into the formula for m

m =
`(11-2)/(4-1)` =
`(9)/(3)` = 3 , then

y = 3x + c ← is the partial equation

to find c , substitute either of the 2 points into the partial equation.

using (1, 2 ) for x and y in the partial equation

2 = 3(1) + c = 3 + c ( subtract 3 from both sides )

- 1 = c

y = 3x - 1 ← equation of linear function

Answer 2

The equation of the linear function passing through the points (1,2) and (4,11) is y = (9/2)x - (5/2). The correct answer is option .

Step-by-step explanation:

The correct answer is option B) y = (9/2)x - (5/2).

To find the equation of the linear function passing through the points (1,2) and (4,11), we can use the formula for a linear function: y = mx + b, where m is the slope and b is the y-intercept.

First, we need to find the slope (m). The slope is calculated as the change in y divided by the change in x between the two points:

m = (11 - 2) / (4 - 1) = 9 / 3 = 3.

Next, we can substitute one of the points (1,2) into the equation to find the y-intercept (b):

2 = 3(1) + b => b = -1.

Plugging the values of m and b into the equation, we get y = (9/2)x - (5/2).

The correct answer is option C, which is y = 3x - 1. To find the equation of a linear function that passes through two points, you can use the formula for the slope (m) which is (y2 - y1) / (x2 - x1). For the points (1,2) and (4,11), the slope is (11 - 2) / (4 - 1) = 9 / 3 = 3. Now, using the slope and one of the points, you can use the point-slope form to find the equation: y - y1 = m(x - x1). Plugging in the values gives us y - 2 = 3(x - 1), which simplifies to y = 3x - 1.