Answer:
y = 5
Step-by-step explanation:
Calculate the slope m using the slope formula
m =
with (x₁, y₁ ) = (7, 5) and (x₂, y₂ ) = (- 9, 5)
m = =
= 0
This means the line is horizontal and parallel to the x- axis with equation
y = c
where c is the value of the y- coordinates the line passes through.
The line passes through (7, 5) and (- 9, 5) with y- coordinates 5, thus
y = 5 ← equation of line
Linear function rule in terms of x and y for this line is y = x + 12
<em><u>Solution:</u></em>
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
<em><u>The slope intercept form is given as:</u></em>
y = mx + c
Where "m" is the slope of line and "c" is the y - intercept
Let us first find slope of line
<em><u>The slope "m" of a line is given as:</u></em>
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