1

Problem

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

2

Step

The points are

\$x_1, y_1 = 4,x\$ and \$x_2, y_2 = -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

In this case, we have the points A(4, x) and B(-5, 9), so the slope (m) is:

\$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

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

Correct 18.00

10

Choice-B

This option is incorrect, as it does not satisfy the equation

Wrong 14.00

11

Choice-C

This option is incorrect, as x=18 is the only valid solution

Wrong 15.00

12

Choice-D

This option is incorrect and does not satisfy the slope equation

Wrong 17.00

13

Answer

Option

A

14

Sumup

Please summarize choices