Question

Consider the line that passes through the points (4, -3) and (2, -1). Below are two different equations. Identify the true statement concerning both equations.


Equation #1 Equation #2
y - 3 = -1(x + 4) y - 1 = -1(x + 2)

Only equation #1 represents the line that passes through the two given points.

Only equation #2 represents the line that passes through the two given points.

Both equation #1 and equation #2 represent the line that passes through the two given points.

Neither equation #1 nor equation #2 represents the line that passes through the two

Answer 1

try finding the slope of the line that passes between the two points,(4, -3) and (2, -1).

Once you have found the slope, check equation 1 and 2 to see if either has that same slope.

Answer 2

how would i find the slope

Answer 3

slope is (-3 -(-1) / (4 - 2) change in the y values divided by change in the x values.


Another different approach is to take the 2 points one at a time, and to try the x and y values from each point as inputs into each line. If you put the values in and the equation works, it means that point is on the line. If you put the points in and you get nonsense, then the point is not on the line.

Answer 4

ok

Answer 5

Equation #1 Equation #2
y - 3 = -1(x + 4) y - 1 = -1(x + 2)
1 - 3 = -1(-3 + 4) 2 - 1 = -1(7 + 2)

Answer 6

Are you seeing "nonsense" in those equations?

Answer 7

#1
1 - 3 = -1(-3 + 4)
-2 = -3 + -4

Answer 8

-2 = -3 - 4
+4 +4
2 = -3
i see nonsense in #1

Answer 9

hold on... you mixed it up a little, although you are good at spotting nonsense :)

Answer 10

ok

Answer 11

Let's try Eq # 1 again, using the 2nd point, (2, -1):

y - 3 = -1(x + 4)

(-1) - 3 = -1(2 + 4)
-4 = -1(6)
-4 = -6
nonsense... therefore, point (2,-1) is NOT on the line shown in Eq # 1

Answer 12

ok

Answer 13

if you wanted, you could also try the first point, (4, -3) on the same Eq # 1, but it doesn't matter for Eq # 1... if the second point isn't even on the line, it doesn't matter if the other point is on the line... the line itself doesn't go through both points.

We still need to check Eq # 2

Answer 14

Equation #2
y - 1 = -1(x + 2)
2 - 1 = -1(-1 + 2)
3 = 1 - 2
+2 +2
5 = 1
Nonsense

Answer 15

again, close, but be careful... you chose point (2, -1), but when you put it in the equation, you substituted in the (-1) term as the "x" on the right side... the point is (x,y), so you need to put in x = 2 on the right side and y = -1 on the left.

It will probably still be nonsense, but please be careful substituting in the (x,y)

Answer 16

ok but is the answer D???