Question

Find the equation of the linear function passing through (2,3) and (5,12)

Answer 1

y = 3x - 3 is the equation of the linear function passing through (2, 3) and (5, 12)

Solution:

Given that we have to find the equation of linear function passing through (2, 3) and (5, 12)

The formula y = mx + b is said to be a linear function

Where "m" is the slope of line and "b" is the y - intercept

Let us first find the slope of line

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

`\text {Here } x_(1)=2 ; y_(1)=3 ; x_(2)=5 ; y_(2)=12`

Substituting values we get,

`m=(12-3)/(5-2)=(9)/(3)=3`

Thus slope of line is m = 3

To find the y - intercept, substitute m = 3 and (x, y) = (2, 3) in y = mx + b

3 = 3(2) + b

3 = 6 + b

b = 3 - 6

b = -3

Thus the required equation of linear function is:

Substitute m = 3 and b = -3 in formula

y = mx + b

y = 3x - 3

Thus the equation of linear function is found