video explanation

text explanation

we are told that the slope is m = .  think about what that means: that's a rise of 1 and a run of 2, in other words, to the right 2 and up 1.  if we go the other way, that would be to left 2 and down 1.  

start at (0, 5), which is the y-intercept.   

right 2 and up 1  (2, 6) 

right 2 and up 1  (4, 7) 

right 2 and up 1  (6, 8)

right 2 and up 1  (8, 9) 

all those are points on the line.  we see that (b) is on the line, so that can't be the answer.  

if we start at (2, 6) and go right 1 and up , we land at (3, 6.5), which is also on the line, so (c) can't be the answer.  

now, go back to (0, 5) and move to the left to hit the negative values of x.  

left 2 and down 1  (–2, 4)

left 2 and down 1  (–4, 3)

left 2 and down 1  (–6, 2)

left 2 and down 1  (–8, 1)

left 2 and down 1  (–10, 0)

all those point are on the line.  we see that (a) & (e) are on the line, so these can be the answer.  

we have eliminated four answers, leaving only (d).  notice that the line passes through (–2, 4), so it would be impossible also to pass through (–2, 2) directly below it.  

answer = (d) 

faq: can we solve this using y = mx + b?  

yes.  using a formula is slower and more time-consuming route than the intuitive method above, but it will lead to the correct answer.  

the equation for a line is:

y = mx + b

where m is the slope and b is the y-intercept. here, we are told that line k passes through the point (0,5), which means that the y-intercept is 5. so the formula for line k is:

y = x + 5

now, we can plug in the answer choices for (x,y), and see which one doesn't fit in the equation:

(a) (–10, 0) --> x = –10, y = 0

0 = (–10) + 5

0 = –5 + 5

this satisfies the equation, so (–10, 0) lies on line k.

(b) (8, 9) --> x = 8, y = 9

9 = (8) + 5

9 = 4 + 5

this works.

(c) (3, 6.5) --> x = 3, y = 6.5

6.5 = (3) + 5

6.5 = 1.5 + 5

this works.

(d) (–2, 2) --> x = -2, y = 2

2 = (–2) + 5

2 = –1 + 5

2 = 4

this clearly is not true, so (–2, 2) does not lie on line k.

answer = (d)