Accuplacer Practice Test

An equation of the line that contains the origin and the point (1, 2) is

1. 2y = x

2. y = x - 1

3. y = 2x + 1

4. y/2 = x - 1

The correct answer is: 2y = x

To find the equation of the line that contains the origin (0,0) and the point (1,2), we can use the point-slope form of the equation of a line which is \( y - y_1 = m(x - x_1) \), where \( (x_1, y_1) \) is a point on the line and \( m \) is the slope of the line. Here, the point (1,2) lies on the line. We calculate the slope using the formula \( m = \dfrac{y_2 - y_1}{x_2 - x_1} \) by substituting the coordinates of the two points: \( m = \dfrac{2 - 0}{1 - 0} = 2 \). Now, we substitute the slope and the given point (1,2) into the point-slope form: \( y - 2 = 2(x - 1) \). Upon simplifying this equation, we get \( y = 2x - 2 \), or in the form given in choice A: \( 2y = x \). Hence, choice A is the correct answer. The