Question

I need help with my homework, the information given to me wasn't helping.

Answer 1

1)  This is not a linear equation as it curves and thus has acceleration and thus its velocity is not constant.  You COULD find a linear least squares equation, but I do not think that that is what they want you to do, and the least squares regression is still only an approximation...so I would say that you cannot write a linear equation for the graph.

2)  The y-intercept is the value of y when x=0, and this point is clearly marked as the point (0,1)

3)  The slope of a line can be found using any two points on the line and it will be equal to:

m=slope=(y2-y1)/(x2-x1)...in this case:

m=(2-1)/(2--3)=1/5 so the line has a slope of 1/5

4)  To find the y-intercept precisely we start with the slope that we found earlier and use that value in the slope-intercept form of a line, y=mx+b, and since m=1/5 we have:

y=x/5+b, where b is the y-intercept and using (2,2) we can solve for b...

2=2/5+b

10/5=2/5+b

b=8/5 or if you prefer 1 3/5 or 1.6

So the y-intercept is 8/5, 1 3/5, or 1.6 depending on how you'd like to use it.

5)  We have already found b and m of the y=mx+b so the equation of this line  is:

y=x/5+8/5 or more neatly

y=(x+8)/5