If (-3,-1) is a point line on the line with m=2 then: -2,1 and (-4,-3) must be on the line.

Question

If (-3,-1) is a point line on the line with m=2 then: -2,1 and (-4,-3) must be on the line.

Can someone please explain this exercise I don’t get how they found out (-2,1) and (-4,-3) on the line. Thanks

Answer 1

To solve this problem I would:

first : use the point slope form to find the equation of the line.

Second: substitute the two points into the equation to determine if it makes the statement true (does lie on the line) or false (does not lie on the line)

so 1st: (y-y1) = m(x-x1), given (-3,-1) and m=2

(y-(-1)) = 2 (x - (-3))

(y+1) = 2(x+3)

y+1 = 2x +6 (using the distributive property to multiply)

-1 -1 (subtract 1 from each side to solve for y)

y= 2x +5 (This is the equation of our line)

2nd: Using y = 2x +5, Check each point to see if it lies on the line

for (-2,1)

y=2x +5

1= 2(-3) +5

1 = -6 +5

1 = 1

Since both sides are equal, then the point falls on the line.

for (-4,-3)

y = 2x +5

-3 = 2(-4) +5

-3 = -8 +5

-3 = -3

Since both sides are equal, then the point falls on the line.