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

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$\text {Here } x_{1}=2 ; y_{1}=3 ; x_{2}=5 ; y_{2}=12$

Substituting values we get,

$m=\frac{12-3}{5-2}=\frac{9}{3}=3$

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