Respuesta :
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
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]\text {Here } x_{1}=2 ; y_{1}=3 ; x_{2}=5 ; y_{2}=12[/tex]
Substituting values we get,
[tex]m=\frac{12-3}{5-2}=\frac{9}{3}=3[/tex]
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
