Question

A line goes through the points (4,16) Ana (7,19). Write a linear function rule in terms of x and y for this line

Answer 1

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:

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

`\text {Here } x_(1)=4 \text { and } x_(2)=7 \text { and } y_(1)=16 \text { and } y_(2)=19`

`m=(19-16)/(7-4)=(3)/(3)=1`

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