1

Problem

Find the equation of the line passing through the points P(4, 3) and Q(2, -1).

2

Step

The given points are

\$x_1, y_1 = 4, 3\$ and \$x_2, y_2 = 2, -1\$

3

Formula

We can use the point-slope form of a linear equation: \$y - y_1 = m(x - x_1)\$.

4

Formula

First, let’s find the slope (m) using the two given points: \$m = (y_2 - y_1)/(x_2 - x_1)\$.

5

Step

Plug the values into the slope formula and calculate the m:

m = \$(-1 - 3)/(2 - 4)\$

\$m = (\cancel(-4))/(\cancel(-2))\$

m = 2

6

Step

Now that we have the slope (m = 2) and one of the points (P) stem:[(x_1 = 4, y_1 = 3) we can use the point-slope form to write the equation:

\$y - y_1 = m(x - x_1)\$

7

Step

Substitute the values and simplify the equation:

y - 3 = 2(x - 4)

y - 3 = 2x - 8

8

Step

Solve for y:

y = 2x - 8 + 3

y = 2x - 5

9

Solution

So, the equation of the line passing through points P(4, 3) and Q(2, -1) is y = 2x - 5.

10

Sumup

Please summarize steps

Choices

11

Choice-A

This option has the correct slope of 2, but the y-intercept is incorrectly given as 5 instead of -5

Wrong y = 2x + 5

12

Choice-B

This is the correct equation, as it has the correct slope of 2 and y-intercept of -5

Correct y = 2x − 5

13

Choice-C

This option has the right slope of 2, but it assumes a y-intercept of 0, which does not match the line through P(4, 3) and Q(2, -1)

Wrong y = 2x

14

Choice-D

This represents a horizontal line with a slope of 0, which is inconsistent with the calculated slope of 2

Wrong y = 5

15

Answer

Option

B

16

Sumup

Please summarize choices