A line contains the points (0,0) and (1,4).

Select all equations that represent this line.

A.) y = x + 4

B.) y = 4x

C.) (y - 0) = 4(x - 0)

D.) x = 4y

E.) x = 0.25y

F.) y = 4x²

Select all equations that represent this line.

A.) y = x + 4

B.) y = 4x

C.) (y - 0) = 4(x - 0)

D.) x = 4y

E.) x = 0.25y

F.) y = 4x²

If a point lies on a line, when the x and y values of the point are substituted into the equation, it will create a true statement such as 4 = 4 or -3 = -3.

If x = 0 and y = 0, then:

0 = 0 + 4 {substituted}

0 ≠ 4

If x = 0 and y = 0, then:

0 = 4(0) {substituted}

0 = 0 {true statement}

If x = 1 and y = 4, then:

4 = 4(1) {substituted}

4 = 4 {true statement}

it simplifies to y = 4x

If x = 0 and y = 0, then:

0 = 4(0) {substituted}

0 = 0 {true statement}

If x = 1 and y = 4, then:

1 = 4(4) {substituted}

1 ≠ 16

If x = 0 and y = 0, then:

0 = 0.25(0) {substituted}

0 = 0 {true statement}

If x = 1 and y = 4, then:

1 = 0.25(4) {substituted}

1 = 1 {true statement}

If x = 0 and y = 0, then:

0 = 4(0)² {substituted}

0 = 0 {true statement}

If x = 1 and y = 4, then:

4 = 4(1)² {substituted}

4 = 4 {true statement}

**Given points are (0,0) → x = 0 and y = 0**

and (1,4) → x = 1 and y = 4and (1,4) → x = 1 and y = 4

__For line A.) y = x + 4__If x = 0 and y = 0, then:

0 = 0 + 4 {substituted}

0 ≠ 4

**Line A does**__not__contain the points**For line B.) y = 4x**If x = 0 and y = 0, then:

0 = 4(0) {substituted}

0 = 0 {true statement}

If x = 1 and y = 4, then:

4 = 4(1) {substituted}

4 = 4 {true statement}

**Line B contains the points**__For line C.) (y - 0) = 4(x - 0)__it simplifies to y = 4x

*{the same as line B.) above***Line C contains the points**

****__For line D.) x = 4y__If x = 0 and y = 0, then:

0 = 4(0) {substituted}

0 = 0 {true statement}

If x = 1 and y = 4, then:

1 = 4(4) {substituted}

1 ≠ 16

**Line D does**__not__contain the points__For line E.) x = 0.25y__If x = 0 and y = 0, then:

0 = 0.25(0) {substituted}

0 = 0 {true statement}

If x = 1 and y = 4, then:

1 = 0.25(4) {substituted}

1 = 1 {true statement}

**Line E contains the points**__For line F.) y = 4x²__If x = 0 and y = 0, then:

0 = 4(0)² {substituted}

0 = 0 {true statement}

If x = 1 and y = 4, then:

4 = 4(1)² {substituted}

4 = 4 {true statement}

**Line F contains the points**

Equations B, C, E, and F represent this line.Equations B, C, E, and F represent this line.

*- Algebra House*