Respuesta :
Linear function rule in terms of x and y for this line is y = x + 12
Solution:
Given that a line goes through the points (4, 16) and (7, 19)
To find: linear function rule in terms of x and y for this line
A linear function is a function of the form f(x) = ax + b, where a and b are real numbers. Here, a represents the slope of the line, and b represents the y-axis intercept
The slope intercept form is given as:
y = mx + c
Where "m" is the slope of line and "c" is the y - intercept
Let us first find slope of line
The slope "m" of a line is given as:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]\text {Here } x_{1}=4 \text { and } x_{2}=7 \text { and } y_{1}=16 \text { and } y_{2}=19[/tex]
[tex]m=\frac{19-16}{7-4}=\frac{3}{3}=1[/tex]
Thus the slope of line is 1
Substitute m = 1 and (x, y) = (4, 16) in y = mx + c
16 = 1(4) + c
c = 16 - 4 = 12
Substitute c = 12 and m = 1 in slope intercept form
y = 1x + 12
y = x + 12 is the required linear function rule
