Given:
Table for the linear function k.
To find:
The equation for the function.
Solution:
Take any two points from the table.
Let the points are (10, 18) and (30, 58).
Slope of the line:
[tex]$m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Here, [tex]x_1=10, y_1=18, x_2=30, y_2=58[/tex]
[tex]$m=\frac{58-18}{30-10}[/tex]
[tex]$m=\frac{40}{20}[/tex]
m = 2
Using point-slope formula:
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-18=2(x-10)[/tex]
[tex]y-18=2x-20[/tex]
Add 18 on both sides.
[tex]y-18+18=2x-20+18[/tex]
[tex]y=2x-2[/tex]
Replace x by c and y by k.
[tex]k=2c-2[/tex]
The slope-intercept form of the equation of the function is k = 2c - 2.
Answer:
Given:
Table for the linear function k.
To find:
The equation for the function.
Solution:
Take any two points from the table.
Let the points are (10, 18) and (30, 58).
Slope of the line:
Here,
m = 2
Using point-slope formula:
Add 18 on both sides.
Replace x by c and y by k.
The slope-intercept form of the equation of the function is k = 2c - 2.
Step-by-step explanation:
