Question

Equation of line with slope 2 passing through origin:

• A. $y = 2x$
• B. $x = 2y$
• C. $y = x + 2$
• D. $y = 2$

Hint:

Any line passing through the origin will never have a constant term added or subtracted (it will always be in the form $y = mx$).

Answer 1

The Correct Option is A

The problem is to find the equation of a line with a given slope that passes through a specific point. Here, the line has a slope of 2 and it passes through the origin (0,0).

To derive the equation of the line, we can use the point-slope form of a line, given by the formula:

\(y - y_1 = m(x - x_1)\)

where \(m\) is the slope, and \((x_1, y_1)\) is a point on the line.

For this problem:

• Slope \(m = 2\)
• Point \((x_1, y_1) = (0, 0)\)

Plug these values into the point-slope formula:

\(y - 0 = 2(x - 0)\)

Simplify the equation:

\(y = 2x\)

This is the equation of the line in the standard form, and the correct answer is therefore \(y = 2x\).

Let's analyze why the other options are incorrect:

• \(x = 2y\): This would represent a line with a slope of \(\frac{1}{2}\), not 2.
• \(y = x + 2\): This equation has a slope of 1 and an intercept at y=2, not passing through the origin.
• \(y = 2\): This describes a horizontal line, not related to slope 2.

Always remember, the equation of a line in the form \(y = mx + c\) is called the slope-intercept form, where \(m\) is the slope and \(c\) is the y-intercept. For a line passing through the origin, \(c = 0\).