1

Problem

If the slope of a line joining A(4, x) and B(- 5, 9) is 1 then find x.

2

Step

The given

A = (4, x) and B = (- 5, 9)

3

Formula

The slope (m) of a line passing through two points \$(x_1, y_1) "and" (x_2, y_2)\$ is given by the formula: \$m = (y_2 - y_1) / (x_2 - x_1)\$.

4

Step

Plug the values in the fromula:

\$m = (9 - x) / (- 5 - 4)\$

5

Step

Since we know that the slope is 1, we can set the equation equal to 1 and solve for x:

\$1 = (9 - x) / (-5 - 4)\$

\$1 = (9 - x) / (-9)\$

6

Step

Cross-multiply to get rid of the fraction:

\$1 \times (-9) = 9 - x\$

-9 - 9 = - x

⇒ x = 18

7

Solution

Therefore, if the slope of a line joining A(4, x) and B(-5, 9) is 1 then x = 18.

8

Sumup

Please summarize steps

Choices

9

Choice-A

Correct representation of x value to satisfy given slope condition for line AB(4, x) and (- 5, 9) = 1

Correct 18

10

Choice-B

This is incorrect solution obtained from the calculations

Wrong 14

11

Choice-C

This is incorrect solution obtained from the calculations by using the formula

Wrong 15

12

Choice-D

This is incorrect solution obtained from the calculations

Wrong 17

13

Answer

Option

A

14

Sumup

Please summarize choices