Question

Loren solved the equation for b as part of her work to find the equation of a trend line that passes through the points (1, 130) and (10, 149). What error did Loren make?

A. She Should Have Solved 10=9/19(149)+b For B

B. She Should Have Solved 1=19/9(130)+b For B

C. She Should Have Solved 149=19/9(10)+b For B

D. She Should Have Solved 130=9/19(1)+b For B

Thanks For The Help :D

Answer 1

The equation of a straight line is given by:
m(x-x1)=y-y1
where m is the slope
m=(Δ y-axis)/(Δ x-axis)
given points (1,130) and (10,149)
m=(149-130)/(10-1)
=19/9
therefore using point (10,149) which takes the form (x,y) the equation will be:
149=19/9(10)+b
The answer is C.

Answer 2

C. She Should Have Solved 149=19/9(10)+b For B

Let's see about creating out own line and from that pick the right answer. The general form of a line in slope intercept form is
y = ax + b
where
a = slope
b = y intercept.
The slope is the difference in y divided by the difference in x. So
(149 - 130)/(10-1) = 19/9
So the equation we have so far is
y = 19/9 * x + b

And to find the value for b, we substitute a known X and Y pair into the partial equation and solve for b. Looking at the available options, we can immediately eliminate A and D since they have the wrong slope, leaving just options B and C. For option B, it's claiming a Y value of 1 and an X value of 130 which is opposite to the known value of Y=130 and X=1, so option B is wrong. And finally, option C has a Y value of 149 and an X value of 10 which matches a known point of (10,149). So option C is correct.