Question

Write equation of the line containing (6,3) and (4,1)

Group of answer choices

y = -1x + 5

y = 1x - 3

y = 1x + 5

y = -1x + 3

Answer 1

There are two ways to approach this.

The first is to just check with equation works with both points by plugging in x=6 and seeing if you get y=3, from the point (6,3), and then repeating that process with (4,1).

Checking (6,3) on y = -1x+5:

y = -1(6)+5 = -1 -> no good.

Checking (6,3) on y = x-3:

y = 6-3 = 3 -> check

Checking (6,3) on y = x+5:

y = 6+5 = 11 -> no good.

Checking (6,3) on y = -1x+3:

y = -1(6)+3 = -3 -> no good.

So that shows only y = 1x - 3 works, but you should still double check it works for (4,1).

The second option is to construct the equation, which is good to know, in case you don't have a list of equations to check.

For this, you need to calculate the slope, using
`m=(y_2-y_1)/(x_2-x_1)`, and then use that slope to find the y-intercept, (0,b).

Step 1: slope

`m=(1-3)/(4-6) = (-2)/(-2) = 1`

Step 2: find y-intercept

Start by setting up the slope-intercept form with the slope we just found and then plug in one of the points:

`y=1x+b`, which becomes
`3 = 1(6)+b` using (6,3).

Solving this for b, you find b=-3.

Step 3: put it all together:

m = 1 and b = -1 gives you

y = 1x -3

Both ways work and are valid. Context will indicate which one is best.