Question

The slope of a line is 2. The line goes through (10, 5) and (x, 1). Find x.

Answer 1

x = 8

Step-by-step explanation:

calculate the slope of the line through the 2 points using the slope formula , then equate to the slope 2.

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

let (x₁, y₁ ) = (10, 5 ) and (x₂, y₂ ) = (x, 1 )

substitute these values into the formula for m

m =
`(1-5)/(x-10)` =
`(-4)/(x-10)`

equate this expression to m = 2

`(-4)/(x-10)` = 2 ( multiply both sides by (x - 10)

- 4 = 2(x - 10) ← divide both sides by 2

- 2 = x - 10 ( add 10 to both sides )

8 = x

Answer 2

To find the value of x for a line with a slope of 2 that passes through the points (10, 5) and (x, 1), we use the slope formula. After setting up the equation and solving, we find that the answer is x = 8.

Step-by-step explanation:

The student is asking to find the value of x for a line with the slope of 2 that passes through the points (10, 5) and (x, 1). To calculate this, we use the formula for the slope, which is (change in y) / (change in x). We can set up the equation like this:

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

2 = (1 - 5) / (x - 10)

We can solve for x by multiplying both sides by (x - 10) and then isolating x to find its value:

2(x - 10) = 1 - 5

2x - 20 = -4

2x = 16

x = 8

The correct answer is option x = 8.

The slope of a line is given by the formula (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. In this case, we have the slope as 2 and one point (10, 5). Let's call the other point (x, 1). Using the formula, we can set up the equation as (1 - 5) / (x - 10) = 2. Solving for x, we get x = 7. Therefore, the value of x is 7.