Question

Write an equation in slope-intercept form for each table below. Show how you found the slope and y-intercept.

-----------------------------------------
(1):
|x: 0 | 1 | 2 | 3 | 4
|
|y: 0 | 2.5 | 5 | 7.5 | 10
|
-----------------------------------------

Answer 1

`x=1;\ y=2.5\\x=2;\ y= 5\\\\The\ slope-intercept\ form:y=mx+b\\\\subtitute:\\\\ - \left\{\begin{array}{ccc}2.5=1m+b\\5=2m+b\end{array}\right\ \ \ |subtract\ both\ sides\ of\ equations\\--------\\.\ \ \ \ -2.5=-m\\.\ \ \ \ \ m=2.5\\\\subtitute\ value\ of\ m\ to\ the\ equation\ 2.5=1m+b\\\\2.5=2.5+b\\2.5+b=2.5\ \ \ \ |subtract\ 2.5\ from\ both\ sides\\b=0\\\\Therefore,\ answer\ is:\boxed{y=2.5x+0=2.5x}`


`Check:\\x=0;\ y=0\\0=2.5\cdot0\\0=0-correct\\\\x=3;\ y=7.5\\7.5=2.5\cdot3\\7.5=7.5-correct\\\\x=4;\ y=10\\10=2.5\cdot4\\10=10-correct`