Question

Eliza graphed a function representing the arithmetic sequence {−5,5,15,25,35}. She then connected the points to make a line.

If Eliza graphed the function correctly, the line through the points of the function should have _[blank A]_ and _[blank B]_.

Choose one answer for blank A and one for blank B, which correctly completes the previous statement.

1. a slope of 10
2. a y-intercept of (0,−5)
3. a y-intercept at (0,−15)
4. an x-intercept of (10,0)
5. an x-intercept of (−5,0)
6. a slope of 40

Answer 1

Well we are adding by 10 for every 1 increase in x. So slope is 10 / 1 = 10. (1. a slope of 10) is an answer.

We want x = 1 to have y = -5 Slope form is y=mx+b. We know m = 10 bec slope is 10. We have the point (1,-5) on the graph so we solve for b by plugging:

-5 = 10(1) + b and this is b = -15. So graph has function y = 10x-15.

b is the y-intercept so (3. a y-intercept at (0,−15)) is an answer.