3. Is the relationship shown by the data linear? If so, model the data with an equation X | Y 1 ,5| 5,10| 9,15| 13,20|

Accepted Solution

Answer:[tex]y=\frac{5}{4}x+\frac{15}{4}[/tex]Step-by-step explanation: x | y-------1     55   109    1513   20This one is linear because as x goes up by the same number so does y. So the ratio of difference of y to difference of x is the same per pair of points.So a linear equation in slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.To find the slope, I'm going to line up the points vertically and subtract, then put 2nd difference over 1st difference. Like so, ( 1    ,   5)-( 5   ,  10)-----------------4          -5So the slope is 5/4 which makes sense since the y's are going up by 5 each time and the x's are going up by 4 each time.So we have m=5/4. Let's plug that into our y=mx+b.y=5/4 x+bTo find b, we need to use y=5/4 x+b along with one of the given points.Choose; it doesn't matter.  I like (1,5) I guess. y=5/4 x +b with (1,5)5=5/4 (1)+b5=5/4    +bSubtract 5/4 on both sides:5-5/4=b20/4-5/4=b  (Found a common denominator)15/4=bThe y-intercept is 15/4 so b=15/4.So the equation for the line in slope-intercept form is y=5/4 x +15/4.[tex]y=\frac{5}{4}x+\frac{15}{4}[/tex]