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
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.
Given points are (0,0) → x = 0 and y = 0 and (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. Ask Algebra House Comments are closed.

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