1

Problem

Given that the line passes through the points (3, 4) and (5, 8), find the equation of the linear function.

2

Step

The given points are

\$ (x_1,y_1) = (3,4), (x_2,y_2) = (5,8) \$

3

Formula

To find the equation of a linear function given two points, we can use the point-slope form of a linear equation, which is: \$y - y_1 = m(x - x_1)\$.

4

Hint

Where \$(x_1, y_1)\$ are the coordinates of one of the points on the line, and m is the slope of the line.

5

Formula

Slope formula is \$ m = (y_2 - y_1) / (x_2 - x_1) \$.

6

Step

Plug the given points in the slope formula:

\$ m = (8 - 4) / (5 - 3) = \cancel(4)^2/\cancel2 \$

m = 2

7

Step

Use the point (3,4) and then plug the values in the point-slope formula:

\$y - 4 = 2(x - 3) \$

\$y - 4 = 2x - 6 \$

8

Step

To get the equation in slope-intercept form (y = mx + b), we isolate y:

\$y = 2x - 6 + 4 \$

\$y = 2x - 2\$

9

Solution

Therefore, the equation of the linear function is \$y = 2x - 2\$.

10

Sumup

Please summarize steps

Choices

11

Choice-A

This option represents the correct equation of the line passing through the given points, derived from the slope-intercept form with the correct slope and intercept

Correct \$g(x) = 2x - 2\$

12

Choice-B

This option has an incorrect intercept; the slope is correct, but the y-intercept should be -2, not -3

Wrong \$g(x) = 2x - 3\$

13

Choice-C

This option also has an incorrect intercept; the slope is correct, but the y-intercept should be -2, not -4

Wrong \$g(x) = 2x - 4\$

14

Choice-D

This option has an incorrect intercept; the slope is correct, but the y-intercept should be -2, not -5

Wrong \$g(x) = 2x - 5\$

15

Answer

Option

A

16

Sumup

Please summarize choices