Question

A line passes through the points (1, 2) and (4, 4). What is the slope of the line?

A) 1 /4
B) 2 /3
C) 3/ 2
D) 4

Answer 1

The slope of the line passing through the points (1, 2) and (4, 4) is found by dividing the change in y by the change in x, resulting in a slope of 2/3.

Step-by-step explanation:

The slope of a line passing through two points can be calculated using the formula: slope (m) = (change in y) / (change in x), which is (y2 - y1) / (x2 - x1). With the points (1, 2) and (4, 4), we calculate the slope as follows:

You subtract the y-coordinate of the first point from the y-coordinate of the second point to get the change in y: 4 - 2 = 2.

Then, subtract the x-coordinate of the first point from the x-coordinate of the second point to get the change in x: 4 - 1 = 3.

Next, you divide the change in y by the change in x to get the slope: 2 / 3.

The slope of the line is therefore 2/3, which means that option B) 2/3 is the correct answer.

Answer 2

Hello!

To find the slope given two points, we will need to use the slope formula.

Slope formula is
`(y_(2)-y_(1) )/(x_(2)-x_(1))`.

First, we should assign the given points to x1, y1 and x2, y2. The points (1, 2) can be assigned to x1, y1 and (4, 4) to x2, y2.

Now, substitute the assigned ordered pairs into the formula and simplify.

`(4-2)/(4-1) = (2)/(3)`

Therefore, the slope of the line is choice B, 2/3.