1

Problem

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

2

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)\$

3

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)\$

4

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\$

5

Step

Cross-multiply to get rid of the fraction:

\$1×(−9)=9−x\$

\$−9−9=−x\$

⇒ \$x = 18\$

5

Solution

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

6

Sumup

Please summarize Problem, Clue, Hint, Formula, Steps and Solution

Choices

7

Choice-A

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

Correct 18

8

Choice-B

This is incorrect solution obtained from the calculations

Wrong 14

9

Choice-C

This is incorrect solution obtained from the calculations

Wrong 15

10

Choice-D

This is incorrect solution obtained from the calculations

Wrong 17

11

Answer

Option

A

12

Sumup

Please summarize choices